Given the Number 2,148,120, Calculate (Find) All the Factors (All the Divisors) of the Number 2,148,120 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 2,148,120

1. Carry out the prime factorization of the number 2,148,120:

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

2,148,120 = 23 × 35 × 5 × 13 × 17
2,148,120 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 2,148,120

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
prime factor = 3
22 = 4
prime factor = 5
2 × 3 = 6
23 = 8
32 = 9
2 × 5 = 10
22 × 3 = 12
prime factor = 13
3 × 5 = 15
prime factor = 17
2 × 32 = 18
22 × 5 = 20
23 × 3 = 24
2 × 13 = 26
33 = 27
2 × 3 × 5 = 30
2 × 17 = 34
22 × 32 = 36
3 × 13 = 39
23 × 5 = 40
32 × 5 = 45
3 × 17 = 51
22 × 13 = 52
2 × 33 = 54
22 × 3 × 5 = 60
5 × 13 = 65
22 × 17 = 68
23 × 32 = 72
2 × 3 × 13 = 78
34 = 81
5 × 17 = 85
2 × 32 × 5 = 90
2 × 3 × 17 = 102
23 × 13 = 104
22 × 33 = 108
32 × 13 = 117
23 × 3 × 5 = 120
2 × 5 × 13 = 130
33 × 5 = 135
23 × 17 = 136
32 × 17 = 153
22 × 3 × 13 = 156
2 × 34 = 162
2 × 5 × 17 = 170
22 × 32 × 5 = 180
3 × 5 × 13 = 195
22 × 3 × 17 = 204
23 × 33 = 216
13 × 17 = 221
2 × 32 × 13 = 234
35 = 243
3 × 5 × 17 = 255
22 × 5 × 13 = 260
2 × 33 × 5 = 270
2 × 32 × 17 = 306
23 × 3 × 13 = 312
22 × 34 = 324
22 × 5 × 17 = 340
33 × 13 = 351
23 × 32 × 5 = 360
2 × 3 × 5 × 13 = 390
34 × 5 = 405
23 × 3 × 17 = 408
2 × 13 × 17 = 442
33 × 17 = 459
22 × 32 × 13 = 468
2 × 35 = 486
2 × 3 × 5 × 17 = 510
23 × 5 × 13 = 520
22 × 33 × 5 = 540
32 × 5 × 13 = 585
22 × 32 × 17 = 612
23 × 34 = 648
3 × 13 × 17 = 663
23 × 5 × 17 = 680
2 × 33 × 13 = 702
32 × 5 × 17 = 765
22 × 3 × 5 × 13 = 780
2 × 34 × 5 = 810
22 × 13 × 17 = 884
2 × 33 × 17 = 918
23 × 32 × 13 = 936
22 × 35 = 972
22 × 3 × 5 × 17 = 1,020
34 × 13 = 1,053
23 × 33 × 5 = 1,080
5 × 13 × 17 = 1,105
2 × 32 × 5 × 13 = 1,170
35 × 5 = 1,215
23 × 32 × 17 = 1,224
2 × 3 × 13 × 17 = 1,326
34 × 17 = 1,377
22 × 33 × 13 = 1,404
This list continues below...

... This list continues from above
2 × 32 × 5 × 17 = 1,530
23 × 3 × 5 × 13 = 1,560
22 × 34 × 5 = 1,620
33 × 5 × 13 = 1,755
23 × 13 × 17 = 1,768
22 × 33 × 17 = 1,836
23 × 35 = 1,944
32 × 13 × 17 = 1,989
23 × 3 × 5 × 17 = 2,040
2 × 34 × 13 = 2,106
2 × 5 × 13 × 17 = 2,210
33 × 5 × 17 = 2,295
22 × 32 × 5 × 13 = 2,340
2 × 35 × 5 = 2,430
22 × 3 × 13 × 17 = 2,652
2 × 34 × 17 = 2,754
23 × 33 × 13 = 2,808
22 × 32 × 5 × 17 = 3,060
35 × 13 = 3,159
23 × 34 × 5 = 3,240
3 × 5 × 13 × 17 = 3,315
2 × 33 × 5 × 13 = 3,510
23 × 33 × 17 = 3,672
2 × 32 × 13 × 17 = 3,978
35 × 17 = 4,131
22 × 34 × 13 = 4,212
22 × 5 × 13 × 17 = 4,420
2 × 33 × 5 × 17 = 4,590
23 × 32 × 5 × 13 = 4,680
22 × 35 × 5 = 4,860
34 × 5 × 13 = 5,265
23 × 3 × 13 × 17 = 5,304
22 × 34 × 17 = 5,508
33 × 13 × 17 = 5,967
23 × 32 × 5 × 17 = 6,120
2 × 35 × 13 = 6,318
2 × 3 × 5 × 13 × 17 = 6,630
34 × 5 × 17 = 6,885
22 × 33 × 5 × 13 = 7,020
22 × 32 × 13 × 17 = 7,956
2 × 35 × 17 = 8,262
23 × 34 × 13 = 8,424
23 × 5 × 13 × 17 = 8,840
22 × 33 × 5 × 17 = 9,180
23 × 35 × 5 = 9,720
32 × 5 × 13 × 17 = 9,945
2 × 34 × 5 × 13 = 10,530
23 × 34 × 17 = 11,016
2 × 33 × 13 × 17 = 11,934
22 × 35 × 13 = 12,636
22 × 3 × 5 × 13 × 17 = 13,260
2 × 34 × 5 × 17 = 13,770
23 × 33 × 5 × 13 = 14,040
35 × 5 × 13 = 15,795
23 × 32 × 13 × 17 = 15,912
22 × 35 × 17 = 16,524
34 × 13 × 17 = 17,901
23 × 33 × 5 × 17 = 18,360
2 × 32 × 5 × 13 × 17 = 19,890
35 × 5 × 17 = 20,655
22 × 34 × 5 × 13 = 21,060
22 × 33 × 13 × 17 = 23,868
23 × 35 × 13 = 25,272
23 × 3 × 5 × 13 × 17 = 26,520
22 × 34 × 5 × 17 = 27,540
33 × 5 × 13 × 17 = 29,835
2 × 35 × 5 × 13 = 31,590
23 × 35 × 17 = 33,048
2 × 34 × 13 × 17 = 35,802
22 × 32 × 5 × 13 × 17 = 39,780
2 × 35 × 5 × 17 = 41,310
23 × 34 × 5 × 13 = 42,120
23 × 33 × 13 × 17 = 47,736
35 × 13 × 17 = 53,703
23 × 34 × 5 × 17 = 55,080
2 × 33 × 5 × 13 × 17 = 59,670
22 × 35 × 5 × 13 = 63,180
22 × 34 × 13 × 17 = 71,604
23 × 32 × 5 × 13 × 17 = 79,560
22 × 35 × 5 × 17 = 82,620
34 × 5 × 13 × 17 = 89,505
2 × 35 × 13 × 17 = 107,406
22 × 33 × 5 × 13 × 17 = 119,340
23 × 35 × 5 × 13 = 126,360
23 × 34 × 13 × 17 = 143,208
23 × 35 × 5 × 17 = 165,240
2 × 34 × 5 × 13 × 17 = 179,010
22 × 35 × 13 × 17 = 214,812
23 × 33 × 5 × 13 × 17 = 238,680
35 × 5 × 13 × 17 = 268,515
22 × 34 × 5 × 13 × 17 = 358,020
23 × 35 × 13 × 17 = 429,624
2 × 35 × 5 × 13 × 17 = 537,030
23 × 34 × 5 × 13 × 17 = 716,040
22 × 35 × 5 × 13 × 17 = 1,074,060
23 × 35 × 5 × 13 × 17 = 2,148,120

The final answer:
(scroll down)

2,148,120 has 192 factors (divisors):
1; 2; 3; 4; 5; 6; 8; 9; 10; 12; 13; 15; 17; 18; 20; 24; 26; 27; 30; 34; 36; 39; 40; 45; 51; 52; 54; 60; 65; 68; 72; 78; 81; 85; 90; 102; 104; 108; 117; 120; 130; 135; 136; 153; 156; 162; 170; 180; 195; 204; 216; 221; 234; 243; 255; 260; 270; 306; 312; 324; 340; 351; 360; 390; 405; 408; 442; 459; 468; 486; 510; 520; 540; 585; 612; 648; 663; 680; 702; 765; 780; 810; 884; 918; 936; 972; 1,020; 1,053; 1,080; 1,105; 1,170; 1,215; 1,224; 1,326; 1,377; 1,404; 1,530; 1,560; 1,620; 1,755; 1,768; 1,836; 1,944; 1,989; 2,040; 2,106; 2,210; 2,295; 2,340; 2,430; 2,652; 2,754; 2,808; 3,060; 3,159; 3,240; 3,315; 3,510; 3,672; 3,978; 4,131; 4,212; 4,420; 4,590; 4,680; 4,860; 5,265; 5,304; 5,508; 5,967; 6,120; 6,318; 6,630; 6,885; 7,020; 7,956; 8,262; 8,424; 8,840; 9,180; 9,720; 9,945; 10,530; 11,016; 11,934; 12,636; 13,260; 13,770; 14,040; 15,795; 15,912; 16,524; 17,901; 18,360; 19,890; 20,655; 21,060; 23,868; 25,272; 26,520; 27,540; 29,835; 31,590; 33,048; 35,802; 39,780; 41,310; 42,120; 47,736; 53,703; 55,080; 59,670; 63,180; 71,604; 79,560; 82,620; 89,505; 107,406; 119,340; 126,360; 143,208; 165,240; 179,010; 214,812; 238,680; 268,515; 358,020; 429,624; 537,030; 716,040; 1,074,060 and 2,148,120
out of which 5 prime factors: 2; 3; 5; 13 and 17
2,148,120 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):

» What are all the proper, improper and prime factors (divisors) of the number 2,148,106?

» What are all the proper, improper and prime factors (divisors) of the number 2,148,131?


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".