Given the Number 1,020,000, Calculate (Find) All the Factors (All the Divisors) of the Number 1,020,000 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 1,020,000

1. Carry out the prime factorization of the number 1,020,000:

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


1,020,000 = 25 × 3 × 54 × 17
1,020,000 is not a prime number but a composite one.


* 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 1,020,000

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
prime factor = 3
22 = 4
prime factor = 5
2 × 3 = 6
23 = 8
2 × 5 = 10
22 × 3 = 12
3 × 5 = 15
24 = 16
prime factor = 17
22 × 5 = 20
23 × 3 = 24
52 = 25
2 × 3 × 5 = 30
25 = 32
2 × 17 = 34
23 × 5 = 40
24 × 3 = 48
2 × 52 = 50
3 × 17 = 51
22 × 3 × 5 = 60
22 × 17 = 68
3 × 52 = 75
24 × 5 = 80
5 × 17 = 85
25 × 3 = 96
22 × 52 = 100
2 × 3 × 17 = 102
23 × 3 × 5 = 120
53 = 125
23 × 17 = 136
2 × 3 × 52 = 150
25 × 5 = 160
2 × 5 × 17 = 170
23 × 52 = 200
22 × 3 × 17 = 204
24 × 3 × 5 = 240
2 × 53 = 250
3 × 5 × 17 = 255
24 × 17 = 272
22 × 3 × 52 = 300
22 × 5 × 17 = 340
3 × 53 = 375
24 × 52 = 400
23 × 3 × 17 = 408
52 × 17 = 425
25 × 3 × 5 = 480
22 × 53 = 500
2 × 3 × 5 × 17 = 510
25 × 17 = 544
23 × 3 × 52 = 600
54 = 625
23 × 5 × 17 = 680
2 × 3 × 53 = 750
25 × 52 = 800
24 × 3 × 17 = 816
2 × 52 × 17 = 850
23 × 53 = 1,000
This list continues below...

... This list continues from above
22 × 3 × 5 × 17 = 1,020
24 × 3 × 52 = 1,200
2 × 54 = 1,250
3 × 52 × 17 = 1,275
24 × 5 × 17 = 1,360
22 × 3 × 53 = 1,500
25 × 3 × 17 = 1,632
22 × 52 × 17 = 1,700
3 × 54 = 1,875
24 × 53 = 2,000
23 × 3 × 5 × 17 = 2,040
53 × 17 = 2,125
25 × 3 × 52 = 2,400
22 × 54 = 2,500
2 × 3 × 52 × 17 = 2,550
25 × 5 × 17 = 2,720
23 × 3 × 53 = 3,000
23 × 52 × 17 = 3,400
2 × 3 × 54 = 3,750
25 × 53 = 4,000
24 × 3 × 5 × 17 = 4,080
2 × 53 × 17 = 4,250
23 × 54 = 5,000
22 × 3 × 52 × 17 = 5,100
24 × 3 × 53 = 6,000
3 × 53 × 17 = 6,375
24 × 52 × 17 = 6,800
22 × 3 × 54 = 7,500
25 × 3 × 5 × 17 = 8,160
22 × 53 × 17 = 8,500
24 × 54 = 10,000
23 × 3 × 52 × 17 = 10,200
54 × 17 = 10,625
25 × 3 × 53 = 12,000
2 × 3 × 53 × 17 = 12,750
25 × 52 × 17 = 13,600
23 × 3 × 54 = 15,000
23 × 53 × 17 = 17,000
25 × 54 = 20,000
24 × 3 × 52 × 17 = 20,400
2 × 54 × 17 = 21,250
22 × 3 × 53 × 17 = 25,500
24 × 3 × 54 = 30,000
3 × 54 × 17 = 31,875
24 × 53 × 17 = 34,000
25 × 3 × 52 × 17 = 40,800
22 × 54 × 17 = 42,500
23 × 3 × 53 × 17 = 51,000
25 × 3 × 54 = 60,000
2 × 3 × 54 × 17 = 63,750
25 × 53 × 17 = 68,000
23 × 54 × 17 = 85,000
24 × 3 × 53 × 17 = 102,000
22 × 3 × 54 × 17 = 127,500
24 × 54 × 17 = 170,000
25 × 3 × 53 × 17 = 204,000
23 × 3 × 54 × 17 = 255,000
25 × 54 × 17 = 340,000
24 × 3 × 54 × 17 = 510,000
25 × 3 × 54 × 17 = 1,020,000

The final answer:
(scroll down)

1,020,000 has 120 factors (divisors):
1; 2; 3; 4; 5; 6; 8; 10; 12; 15; 16; 17; 20; 24; 25; 30; 32; 34; 40; 48; 50; 51; 60; 68; 75; 80; 85; 96; 100; 102; 120; 125; 136; 150; 160; 170; 200; 204; 240; 250; 255; 272; 300; 340; 375; 400; 408; 425; 480; 500; 510; 544; 600; 625; 680; 750; 800; 816; 850; 1,000; 1,020; 1,200; 1,250; 1,275; 1,360; 1,500; 1,632; 1,700; 1,875; 2,000; 2,040; 2,125; 2,400; 2,500; 2,550; 2,720; 3,000; 3,400; 3,750; 4,000; 4,080; 4,250; 5,000; 5,100; 6,000; 6,375; 6,800; 7,500; 8,160; 8,500; 10,000; 10,200; 10,625; 12,000; 12,750; 13,600; 15,000; 17,000; 20,000; 20,400; 21,250; 25,500; 30,000; 31,875; 34,000; 40,800; 42,500; 51,000; 60,000; 63,750; 68,000; 85,000; 102,000; 127,500; 170,000; 204,000; 255,000; 340,000; 510,000 and 1,020,000
out of which 4 prime factors: 2; 3; 5 and 17
1,020,000 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.


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".