Given the Number 748,000,000, Calculate (Find) All the Factors (All the Divisors) of the Number 748,000,000 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 748,000,000

1. Carry out the prime factorization of the number 748,000,000:

The prime factorization of a number: finding the prime numbers that multiply together to make that number.

748,000,000 = 28 × 56 × 11 × 17
748,000,000 is not a prime number but a composite one.

» Online calculator. Check whether a number is prime or not. The prime factorization of composite numbers

* Prime number: a natural number that is divisible (divided evenly) only by 1 and itself. A prime number has exactly two factors: 1 and the number itself.
* Composite number: a natural number that has at least one other factor than 1 and itself.


2. Multiply the prime factors of the number 748,000,000

Multiply the prime factors involved in the prime factorization of the number in all their unique combinations, that give different results.

Also consider the exponents of these prime factors.

Also add 1 to the list of factors (divisors). All the numbers are divisible by 1.


All the factors (divisors) are listed below - in ascending order

The list of factors (divisors):

neither prime nor composite = 1
prime factor = 2
22 = 4
prime factor = 5
23 = 8
2 × 5 = 10
prime factor = 11
24 = 16
prime factor = 17
22 × 5 = 20
2 × 11 = 22
52 = 25
25 = 32
2 × 17 = 34
23 × 5 = 40
22 × 11 = 44
2 × 52 = 50
5 × 11 = 55
26 = 64
22 × 17 = 68
24 × 5 = 80
5 × 17 = 85
23 × 11 = 88
22 × 52 = 100
2 × 5 × 11 = 110
53 = 125
27 = 128
23 × 17 = 136
25 × 5 = 160
2 × 5 × 17 = 170
24 × 11 = 176
11 × 17 = 187
23 × 52 = 200
22 × 5 × 11 = 220
2 × 53 = 250
28 = 256
24 × 17 = 272
52 × 11 = 275
26 × 5 = 320
22 × 5 × 17 = 340
25 × 11 = 352
2 × 11 × 17 = 374
24 × 52 = 400
52 × 17 = 425
23 × 5 × 11 = 440
22 × 53 = 500
25 × 17 = 544
2 × 52 × 11 = 550
54 = 625
27 × 5 = 640
23 × 5 × 17 = 680
26 × 11 = 704
22 × 11 × 17 = 748
25 × 52 = 800
2 × 52 × 17 = 850
24 × 5 × 11 = 880
5 × 11 × 17 = 935
23 × 53 = 1,000
26 × 17 = 1,088
22 × 52 × 11 = 1,100
2 × 54 = 1,250
28 × 5 = 1,280
24 × 5 × 17 = 1,360
53 × 11 = 1,375
27 × 11 = 1,408
23 × 11 × 17 = 1,496
26 × 52 = 1,600
22 × 52 × 17 = 1,700
25 × 5 × 11 = 1,760
2 × 5 × 11 × 17 = 1,870
24 × 53 = 2,000
53 × 17 = 2,125
27 × 17 = 2,176
23 × 52 × 11 = 2,200
22 × 54 = 2,500
25 × 5 × 17 = 2,720
2 × 53 × 11 = 2,750
28 × 11 = 2,816
24 × 11 × 17 = 2,992
55 = 3,125
27 × 52 = 3,200
23 × 52 × 17 = 3,400
26 × 5 × 11 = 3,520
22 × 5 × 11 × 17 = 3,740
25 × 53 = 4,000
2 × 53 × 17 = 4,250
28 × 17 = 4,352
24 × 52 × 11 = 4,400
52 × 11 × 17 = 4,675
23 × 54 = 5,000
26 × 5 × 17 = 5,440
22 × 53 × 11 = 5,500
25 × 11 × 17 = 5,984
2 × 55 = 6,250
28 × 52 = 6,400
24 × 52 × 17 = 6,800
54 × 11 = 6,875
27 × 5 × 11 = 7,040
23 × 5 × 11 × 17 = 7,480
26 × 53 = 8,000
22 × 53 × 17 = 8,500
25 × 52 × 11 = 8,800
2 × 52 × 11 × 17 = 9,350
24 × 54 = 10,000
54 × 17 = 10,625
27 × 5 × 17 = 10,880
23 × 53 × 11 = 11,000
26 × 11 × 17 = 11,968
22 × 55 = 12,500
25 × 52 × 17 = 13,600
2 × 54 × 11 = 13,750
28 × 5 × 11 = 14,080
24 × 5 × 11 × 17 = 14,960
56 = 15,625
27 × 53 = 16,000
23 × 53 × 17 = 17,000
26 × 52 × 11 = 17,600
22 × 52 × 11 × 17 = 18,700
25 × 54 = 20,000
2 × 54 × 17 = 21,250
28 × 5 × 17 = 21,760
24 × 53 × 11 = 22,000
53 × 11 × 17 = 23,375
27 × 11 × 17 = 23,936
23 × 55 = 25,000
26 × 52 × 17 = 27,200
This list continues below...

... This list continues from above
22 × 54 × 11 = 27,500
25 × 5 × 11 × 17 = 29,920
2 × 56 = 31,250
28 × 53 = 32,000
24 × 53 × 17 = 34,000
55 × 11 = 34,375
27 × 52 × 11 = 35,200
23 × 52 × 11 × 17 = 37,400
26 × 54 = 40,000
22 × 54 × 17 = 42,500
25 × 53 × 11 = 44,000
2 × 53 × 11 × 17 = 46,750
28 × 11 × 17 = 47,872
24 × 55 = 50,000
55 × 17 = 53,125
27 × 52 × 17 = 54,400
23 × 54 × 11 = 55,000
26 × 5 × 11 × 17 = 59,840
22 × 56 = 62,500
25 × 53 × 17 = 68,000
2 × 55 × 11 = 68,750
28 × 52 × 11 = 70,400
24 × 52 × 11 × 17 = 74,800
27 × 54 = 80,000
23 × 54 × 17 = 85,000
26 × 53 × 11 = 88,000
22 × 53 × 11 × 17 = 93,500
25 × 55 = 100,000
2 × 55 × 17 = 106,250
28 × 52 × 17 = 108,800
24 × 54 × 11 = 110,000
54 × 11 × 17 = 116,875
27 × 5 × 11 × 17 = 119,680
23 × 56 = 125,000
26 × 53 × 17 = 136,000
22 × 55 × 11 = 137,500
25 × 52 × 11 × 17 = 149,600
28 × 54 = 160,000
24 × 54 × 17 = 170,000
56 × 11 = 171,875
27 × 53 × 11 = 176,000
23 × 53 × 11 × 17 = 187,000
26 × 55 = 200,000
22 × 55 × 17 = 212,500
25 × 54 × 11 = 220,000
2 × 54 × 11 × 17 = 233,750
28 × 5 × 11 × 17 = 239,360
24 × 56 = 250,000
56 × 17 = 265,625
27 × 53 × 17 = 272,000
23 × 55 × 11 = 275,000
26 × 52 × 11 × 17 = 299,200
25 × 54 × 17 = 340,000
2 × 56 × 11 = 343,750
28 × 53 × 11 = 352,000
24 × 53 × 11 × 17 = 374,000
27 × 55 = 400,000
23 × 55 × 17 = 425,000
26 × 54 × 11 = 440,000
22 × 54 × 11 × 17 = 467,500
25 × 56 = 500,000
2 × 56 × 17 = 531,250
28 × 53 × 17 = 544,000
24 × 55 × 11 = 550,000
55 × 11 × 17 = 584,375
27 × 52 × 11 × 17 = 598,400
26 × 54 × 17 = 680,000
22 × 56 × 11 = 687,500
25 × 53 × 11 × 17 = 748,000
28 × 55 = 800,000
24 × 55 × 17 = 850,000
27 × 54 × 11 = 880,000
23 × 54 × 11 × 17 = 935,000
26 × 56 = 1,000,000
22 × 56 × 17 = 1,062,500
25 × 55 × 11 = 1,100,000
2 × 55 × 11 × 17 = 1,168,750
28 × 52 × 11 × 17 = 1,196,800
27 × 54 × 17 = 1,360,000
23 × 56 × 11 = 1,375,000
26 × 53 × 11 × 17 = 1,496,000
25 × 55 × 17 = 1,700,000
28 × 54 × 11 = 1,760,000
24 × 54 × 11 × 17 = 1,870,000
27 × 56 = 2,000,000
23 × 56 × 17 = 2,125,000
26 × 55 × 11 = 2,200,000
22 × 55 × 11 × 17 = 2,337,500
28 × 54 × 17 = 2,720,000
24 × 56 × 11 = 2,750,000
56 × 11 × 17 = 2,921,875
27 × 53 × 11 × 17 = 2,992,000
26 × 55 × 17 = 3,400,000
25 × 54 × 11 × 17 = 3,740,000
28 × 56 = 4,000,000
24 × 56 × 17 = 4,250,000
27 × 55 × 11 = 4,400,000
23 × 55 × 11 × 17 = 4,675,000
25 × 56 × 11 = 5,500,000
2 × 56 × 11 × 17 = 5,843,750
28 × 53 × 11 × 17 = 5,984,000
27 × 55 × 17 = 6,800,000
26 × 54 × 11 × 17 = 7,480,000
25 × 56 × 17 = 8,500,000
28 × 55 × 11 = 8,800,000
24 × 55 × 11 × 17 = 9,350,000
26 × 56 × 11 = 11,000,000
22 × 56 × 11 × 17 = 11,687,500
28 × 55 × 17 = 13,600,000
27 × 54 × 11 × 17 = 14,960,000
26 × 56 × 17 = 17,000,000
25 × 55 × 11 × 17 = 18,700,000
27 × 56 × 11 = 22,000,000
23 × 56 × 11 × 17 = 23,375,000
28 × 54 × 11 × 17 = 29,920,000
27 × 56 × 17 = 34,000,000
26 × 55 × 11 × 17 = 37,400,000
28 × 56 × 11 = 44,000,000
24 × 56 × 11 × 17 = 46,750,000
28 × 56 × 17 = 68,000,000
27 × 55 × 11 × 17 = 74,800,000
25 × 56 × 11 × 17 = 93,500,000
28 × 55 × 11 × 17 = 149,600,000
26 × 56 × 11 × 17 = 187,000,000
27 × 56 × 11 × 17 = 374,000,000
28 × 56 × 11 × 17 = 748,000,000

The final answer:
(scroll down)

748,000,000 has 252 factors (divisors):
1; 2; 4; 5; 8; 10; 11; 16; 17; 20; 22; 25; 32; 34; 40; 44; 50; 55; 64; 68; 80; 85; 88; 100; 110; 125; 128; 136; 160; 170; 176; 187; 200; 220; 250; 256; 272; 275; 320; 340; 352; 374; 400; 425; 440; 500; 544; 550; 625; 640; 680; 704; 748; 800; 850; 880; 935; 1,000; 1,088; 1,100; 1,250; 1,280; 1,360; 1,375; 1,408; 1,496; 1,600; 1,700; 1,760; 1,870; 2,000; 2,125; 2,176; 2,200; 2,500; 2,720; 2,750; 2,816; 2,992; 3,125; 3,200; 3,400; 3,520; 3,740; 4,000; 4,250; 4,352; 4,400; 4,675; 5,000; 5,440; 5,500; 5,984; 6,250; 6,400; 6,800; 6,875; 7,040; 7,480; 8,000; 8,500; 8,800; 9,350; 10,000; 10,625; 10,880; 11,000; 11,968; 12,500; 13,600; 13,750; 14,080; 14,960; 15,625; 16,000; 17,000; 17,600; 18,700; 20,000; 21,250; 21,760; 22,000; 23,375; 23,936; 25,000; 27,200; 27,500; 29,920; 31,250; 32,000; 34,000; 34,375; 35,200; 37,400; 40,000; 42,500; 44,000; 46,750; 47,872; 50,000; 53,125; 54,400; 55,000; 59,840; 62,500; 68,000; 68,750; 70,400; 74,800; 80,000; 85,000; 88,000; 93,500; 100,000; 106,250; 108,800; 110,000; 116,875; 119,680; 125,000; 136,000; 137,500; 149,600; 160,000; 170,000; 171,875; 176,000; 187,000; 200,000; 212,500; 220,000; 233,750; 239,360; 250,000; 265,625; 272,000; 275,000; 299,200; 340,000; 343,750; 352,000; 374,000; 400,000; 425,000; 440,000; 467,500; 500,000; 531,250; 544,000; 550,000; 584,375; 598,400; 680,000; 687,500; 748,000; 800,000; 850,000; 880,000; 935,000; 1,000,000; 1,062,500; 1,100,000; 1,168,750; 1,196,800; 1,360,000; 1,375,000; 1,496,000; 1,700,000; 1,760,000; 1,870,000; 2,000,000; 2,125,000; 2,200,000; 2,337,500; 2,720,000; 2,750,000; 2,921,875; 2,992,000; 3,400,000; 3,740,000; 4,000,000; 4,250,000; 4,400,000; 4,675,000; 5,500,000; 5,843,750; 5,984,000; 6,800,000; 7,480,000; 8,500,000; 8,800,000; 9,350,000; 11,000,000; 11,687,500; 13,600,000; 14,960,000; 17,000,000; 18,700,000; 22,000,000; 23,375,000; 29,920,000; 34,000,000; 37,400,000; 44,000,000; 46,750,000; 68,000,000; 74,800,000; 93,500,000; 149,600,000; 187,000,000; 374,000,000 and 748,000,000
out of which 4 prime factors: 2; 5; 11 and 17
748,000,000 and 1 are sometimes called improper factors, the others are called proper factors (proper divisors).

A quick way to find the factors (the divisors) of a number is to break it down into prime factors.

Then multiply the prime factors and their exponents, if any, in all their different combinations.


Other similar operations of calculating factors (divisors):

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» What are all the proper, improper and prime factors (divisors) of the number 748,000,012?


Calculate all the divisors (factors) of the given numbers

How to calculate (find) all the factors (divisors) of a number:

Break down the number into prime factors. Then multiply its prime factors in all their unique combinations, that give different results.

To calculate the common factors of two numbers:

The common factors (divisors) of two numbers are all the factors of the greatest common factor, gcf.

Calculate the greatest (highest) common factor (divisor) of the two numbers, gcf (hcf, gcd).

Break down the GCF into prime factors. Then multiply its prime factors in all their unique combinations, that give different results.

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The list of all the calculated factors (divisors) of one or two numbers

Factors (divisors), common factors (common divisors), the greatest common factor, GCF (also called the greatest common divisor, GCD, or the highest common factor, HCF)

  • If the number "t" is a factor (divisor) of the number "a" then in the prime factorization of "t" we will only encounter prime factors that also occur in the prime factorization of "a".
  • If there are exponents involved, the maximum value of an exponent for any base of a power that is found in the prime factorization of "t" (powers, or multiplicities) is at most equal to the exponent of the same base that is involved in the prime factorization of "a".
  • Hint: 23 = 2 × 2 × 2 = 8. 2 is called the base and 3 is the exponent. 23 is the power and 8 is the value of the power. We sometimes say that the number 2 is raised to the power of 3.
  • For example, 12 is a factor (divisor) of 120 - the remainder is zero when dividing 120 by 12.
  • Let's look at the prime factorization of both numbers and notice the bases and the exponents that occur in the prime factorization of both numbers:
  • 12 = 2 × 2 × 3 = 22 × 3
  • 120 = 2 × 2 × 2 × 3 × 5 = 23 × 3 × 5
  • 120 contains all the prime factors of 12, and all its bases' exponents are higher than those of 12.
  • If "t" is a common factor (divisor) of "a" and "b", then the prime factorization of "t" contains only the common prime factors involved in the prime factorizations of both "a" and "b".
  • If there are exponents involved, the maximum value of an exponent for any base of a power that is found in the prime factorization of "t" is at most equal to the minimum of the exponents of the same base that is involved in the prime factorization of both "a" and "b".
  • For example, 12 is the common factor of 48 and 360.
  • The remainder is zero when dividing either 48 or 360 by 12.
  • Here there are the prime factorizations of the three numbers, 12, 48 and 360:
  • 12 = 22 × 3
  • 48 = 24 × 3
  • 360 = 23 × 32 × 5
  • Please note that 48 and 360 have more factors (divisors): 2, 3, 4, 6, 8, 12, 24. Among them, 24 is the greatest common factor, GCF (or the greatest common divisor, GCD, or the highest common factor, HCF) of 48 and 360.
  • The greatest common factor, GCF, of two numbers, "a" and "b", is the product of all the common prime factors involved in the prime factorizations of both "a" and "b", taken by the lowest exponents.
  • Based on this rule it is calculated the greatest common factor, GCF, (or the greatest common divisor GCD, HCF) of several numbers, as shown in the example below...
  • GCF, GCD (1,260; 3,024; 5,544) = ?
  • 1,260 = 22 × 32
  • 3,024 = 24 × 32 × 7
  • 5,544 = 23 × 32 × 7 × 11
  • The common prime factors are:
  • 2 - its lowest exponent (multiplicity) is: min.(2; 3; 4) = 2
  • 3 - its lowest exponent (multiplicity) is: min.(2; 2; 2) = 2
  • GCF, GCD (1,260; 3,024; 5,544) = 22 × 32 = 252
  • Coprime numbers:
  • If two numbers "a" and "b" have no other common factors (divisors) than 1, gfc, gcd, hcf (a; b) = 1, then the numbers "a" and "b" are called coprime (or relatively prime).
  • Factors of the GCF
  • If "a" and "b" are not coprime, then every common factor (divisor) of "a" and "b" is a also a factor (divisor) of the greatest common factor, GCF (greatest common divisor, GCD, highest common factor, HCF) of "a" and "b".