0 and 957,000: All the common factors (divisors) and prime factors of the integer numbers

The common factors of numbers 0 and 957,000

The common factors (divisors) of numbers 0 and 957,000 are all the factors (divisors) of their 'greatest (highest) common factor (divisor)'.

Note

Factor of a number A: a number B that when multiplied with another C produces the given number A. Both B and C are factors of A.



Calculate the greatest (highest) common factor (divisor), gcf, hcf, gcd

gcf, hcf, gcd (0; n1) = n1, where n1 an integer, n1 >= 0;

Greatest (highest) common factor (divisor):


gcf, hcf, gcd (0; 957,000) = 957,000;


Zero is divisible by any integer number.




Get the prime factorization of GCF (HCF, GCD)

Prime Factorization of a number: finding the prime numbers that multiply together to make that number.


957,000 = 23 × 3 × 53 × 11 × 29;
957,000 is not a prime, is a composite number.


* Positive integers that are only dividing by themselves and 1 are called prime numbers. A prime number has only two factors: 1 and itself.
* A composite number is a positive integer that has at least one factor (divisor) other than 1 and itself.




Find all the factors (divisors) of the GCF (HCF, GCD)

957,000 = 23 × 3 × 53 × 11 × 29


Get all the combinations (multiplications) of the prime factors of GFC (HCF, GCD) that give different results.


When combining the prime factors also consider their exponents.


Also add 1 to the list of factors (divisors). Any number is divisible by 1.


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



Factors (divisors) list:

neither a prime nor a composite = 1
prime factor = 2
prime factor = 3
22 = 4
prime factor = 5
2 × 3 = 6
23 = 8
2 × 5 = 10
prime factor = 11
22 × 3 = 12
3 × 5 = 15
22 × 5 = 20
continued below...
... continued from above
2 × 11 = 22
23 × 3 = 24
52 = 25
prime factor = 29
2 × 3 × 5 = 30
3 × 11 = 33
23 × 5 = 40
22 × 11 = 44
2 × 52 = 50
5 × 11 = 55
2 × 29 = 58
22 × 3 × 5 = 60
2 × 3 × 11 = 66
3 × 52 = 75
3 × 29 = 87
23 × 11 = 88
22 × 52 = 100
2 × 5 × 11 = 110
22 × 29 = 116
23 × 3 × 5 = 120
53 = 125
22 × 3 × 11 = 132
5 × 29 = 145
2 × 3 × 52 = 150
3 × 5 × 11 = 165
2 × 3 × 29 = 174
23 × 52 = 200
22 × 5 × 11 = 220
23 × 29 = 232
2 × 53 = 250
23 × 3 × 11 = 264
52 × 11 = 275
2 × 5 × 29 = 290
22 × 3 × 52 = 300
11 × 29 = 319
2 × 3 × 5 × 11 = 330
22 × 3 × 29 = 348
3 × 53 = 375
3 × 5 × 29 = 435
23 × 5 × 11 = 440
22 × 53 = 500
2 × 52 × 11 = 550
22 × 5 × 29 = 580
23 × 3 × 52 = 600
2 × 11 × 29 = 638
22 × 3 × 5 × 11 = 660
23 × 3 × 29 = 696
52 × 29 = 725
2 × 3 × 53 = 750
3 × 52 × 11 = 825
2 × 3 × 5 × 29 = 870
3 × 11 × 29 = 957
23 × 53 = 1,000
22 × 52 × 11 = 1,100
23 × 5 × 29 = 1,160
22 × 11 × 29 = 1,276
23 × 3 × 5 × 11 = 1,320
53 × 11 = 1,375
2 × 52 × 29 = 1,450
22 × 3 × 53 = 1,500
5 × 11 × 29 = 1,595
2 × 3 × 52 × 11 = 1,650
22 × 3 × 5 × 29 = 1,740
2 × 3 × 11 × 29 = 1,914
3 × 52 × 29 = 2,175
23 × 52 × 11 = 2,200
23 × 11 × 29 = 2,552
2 × 53 × 11 = 2,750
22 × 52 × 29 = 2,900
23 × 3 × 53 = 3,000
2 × 5 × 11 × 29 = 3,190
22 × 3 × 52 × 11 = 3,300
23 × 3 × 5 × 29 = 3,480
53 × 29 = 3,625
22 × 3 × 11 × 29 = 3,828
3 × 53 × 11 = 4,125
2 × 3 × 52 × 29 = 4,350
3 × 5 × 11 × 29 = 4,785
22 × 53 × 11 = 5,500
23 × 52 × 29 = 5,800
22 × 5 × 11 × 29 = 6,380
23 × 3 × 52 × 11 = 6,600
2 × 53 × 29 = 7,250
23 × 3 × 11 × 29 = 7,656
52 × 11 × 29 = 7,975
2 × 3 × 53 × 11 = 8,250
22 × 3 × 52 × 29 = 8,700
2 × 3 × 5 × 11 × 29 = 9,570
3 × 53 × 29 = 10,875
23 × 53 × 11 = 11,000
23 × 5 × 11 × 29 = 12,760
22 × 53 × 29 = 14,500
2 × 52 × 11 × 29 = 15,950
22 × 3 × 53 × 11 = 16,500
23 × 3 × 52 × 29 = 17,400
22 × 3 × 5 × 11 × 29 = 19,140
2 × 3 × 53 × 29 = 21,750
3 × 52 × 11 × 29 = 23,925
23 × 53 × 29 = 29,000
22 × 52 × 11 × 29 = 31,900
23 × 3 × 53 × 11 = 33,000
23 × 3 × 5 × 11 × 29 = 38,280
53 × 11 × 29 = 39,875
22 × 3 × 53 × 29 = 43,500
2 × 3 × 52 × 11 × 29 = 47,850
23 × 52 × 11 × 29 = 63,800
2 × 53 × 11 × 29 = 79,750
23 × 3 × 53 × 29 = 87,000
22 × 3 × 52 × 11 × 29 = 95,700
3 × 53 × 11 × 29 = 119,625
22 × 53 × 11 × 29 = 159,500
23 × 3 × 52 × 11 × 29 = 191,400
2 × 3 × 53 × 11 × 29 = 239,250
23 × 53 × 11 × 29 = 319,000
22 × 3 × 53 × 11 × 29 = 478,500
23 × 3 × 53 × 11 × 29 = 957,000

Final answer:

0 and 957,000 have 128 common factors (divisors):
1; 2; 3; 4; 5; 6; 8; 10; 11; 12; 15; 20; 22; 24; 25; 29; 30; 33; 40; 44; 50; 55; 58; 60; 66; 75; 87; 88; 100; 110; 116; 120; 125; 132; 145; 150; 165; 174; 200; 220; 232; 250; 264; 275; 290; 300; 319; 330; 348; 375; 435; 440; 500; 550; 580; 600; 638; 660; 696; 725; 750; 825; 870; 957; 1,000; 1,100; 1,160; 1,276; 1,320; 1,375; 1,450; 1,500; 1,595; 1,650; 1,740; 1,914; 2,175; 2,200; 2,552; 2,750; 2,900; 3,000; 3,190; 3,300; 3,480; 3,625; 3,828; 4,125; 4,350; 4,785; 5,500; 5,800; 6,380; 6,600; 7,250; 7,656; 7,975; 8,250; 8,700; 9,570; 10,875; 11,000; 12,760; 14,500; 15,950; 16,500; 17,400; 19,140; 21,750; 23,925; 29,000; 31,900; 33,000; 38,280; 39,875; 43,500; 47,850; 63,800; 79,750; 87,000; 95,700; 119,625; 159,500; 191,400; 239,250; 319,000; 478,500 and 957,000
out of which 5 prime factors: 2; 3; 5; 11 and 29

The key to find the divisors of a number is to build its prime factorization.


Then determine all the different combinations (multiplications) of the prime factors, and their exponents, if any.



More operations of this kind:

Calculator: all the (common) factors (divisors) of numbers

Latest calculated factors (divisors)

common factors (divisors) (0; 957,000) = ? Oct 23 13:44 UTC (GMT)
factors (53,108,002) = ? Oct 23 13:44 UTC (GMT)
factors (887,785) = ? Oct 23 13:44 UTC (GMT)
factors (76,360,028) = ? Oct 23 13:44 UTC (GMT)
factors (561,927) = ? Oct 23 13:44 UTC (GMT)
factors (154) = ? Oct 23 13:44 UTC (GMT)
factors (154) = ? Oct 23 13:44 UTC (GMT)
factors (154) = ? Oct 23 13:44 UTC (GMT)
factors (4,887,547) = ? Oct 23 13:44 UTC (GMT)
common factors (divisors) (27; 45) = ? Oct 23 13:44 UTC (GMT)
factors (2,036,619) = ? Oct 23 13:44 UTC (GMT)
common factors (divisors) (4; 4,696) = ? Oct 23 13:44 UTC (GMT)
common factors (divisors) (20; 8) = ? Oct 23 13:44 UTC (GMT)
common factors (divisors), see more...

Tutoring: 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 "t" is a factor (divisor) of "a" then among the prime factors of "t" will appear only prime factors that also appear on the prime factorization of "a" and the maximum of their exponents (powers, or multiplicities) is at most equal to those involved in the prime factorization of "a".

For example, 12 is a factor (divisor) of 60:

  • 12 = 2 × 2 × 3 = 22 × 3
  • 60 = 2 × 2 × 3 × 5 = 22 × 3 × 5

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 both the prime factorizations of "a" and "b", by lower or at most by equal powers (exponents, or multiplicities).

For example, 12 is the common factor of 48 and 360. After running both numbers' prime factorizations (factoring them down to prime factors):

  • 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, is the product of all prime factors involved in both the prime factorizations of "a" and "b", by the lowest powers (multiplicities).

Based on this rule it is calculated the greatest common factor, GCF, (or greatest common divisor GCD, HCF) of several numbers, as shown in the example below:

  • 1,260 = 22 × 32;
  • 3,024 = 24 × 32 × 7;
  • 5,544 = 23 × 32 × 7 × 11;
  • Common prime factors are: 2 - its lowest power (multiplicity) is min.(2; 3; 4) = 2; 3 - its lowest power (multiplicity) is min.(2; 2; 2) = 2;
  • GCF, GCD (1,260; 3,024; 5,544) = 22 × 32 = 252;

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).

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".


What is a prime number?

What is a composite number?

Prime numbers up to 1,000

Prime numbers up to 10,000

Sieve of Eratosthenes

Euclid's algorithm

Simplifying ordinary (common) math fractions (reducing to lower terms): steps to follow and examples