# 21,000: All the proper, improper and prime factors (divisors) of number

## The fastest way to find all the factors (divisors) of 21,000: 1) Build its prime factorization & 2) Try out all the combinations of the prime factors that give different results

### Factors (divisors) list:

neither a prime nor a composite = 1
prime factor = 2
prime factor = 3
22 = 4
prime factor = 5
2 × 3 = 6
prime factor = 7
23 = 8
2 × 5 = 10
22 × 3 = 12
2 × 7 = 14
3 × 5 = 15
22 × 5 = 20
3 × 7 = 21
23 × 3 = 24
52 = 25
22 × 7 = 28
2 × 3 × 5 = 30
continued below...
... continued from above
5 × 7 = 35
23 × 5 = 40
2 × 3 × 7 = 42
2 × 52 = 50
23 × 7 = 56
22 × 3 × 5 = 60
2 × 5 × 7 = 70
3 × 52 = 75
22 × 3 × 7 = 84
22 × 52 = 100
3 × 5 × 7 = 105
23 × 3 × 5 = 120
53 = 125
22 × 5 × 7 = 140
2 × 3 × 52 = 150
23 × 3 × 7 = 168
52 × 7 = 175
23 × 52 = 200
2 × 3 × 5 × 7 = 210
2 × 53 = 250
23 × 5 × 7 = 280
22 × 3 × 52 = 300
2 × 52 × 7 = 350
3 × 53 = 375
22 × 3 × 5 × 7 = 420
22 × 53 = 500
3 × 52 × 7 = 525
23 × 3 × 52 = 600
22 × 52 × 7 = 700
2 × 3 × 53 = 750
23 × 3 × 5 × 7 = 840
53 × 7 = 875
23 × 53 = 1,000
2 × 3 × 52 × 7 = 1,050
23 × 52 × 7 = 1,400
22 × 3 × 53 = 1,500
2 × 53 × 7 = 1,750
22 × 3 × 52 × 7 = 2,100
3 × 53 × 7 = 2,625
23 × 3 × 53 = 3,000
22 × 53 × 7 = 3,500
23 × 3 × 52 × 7 = 4,200
2 × 3 × 53 × 7 = 5,250
23 × 53 × 7 = 7,000
22 × 3 × 53 × 7 = 10,500
23 × 3 × 53 × 7 = 21,000

## Latest calculated factors (divisors)

 factors (21,000) = ? Sep 23 09:22 UTC (GMT) factors (982,134) = ? Sep 23 09:22 UTC (GMT) common factors (divisors) (3,233,736; 4,115,664) = ? Sep 23 09:22 UTC (GMT) factors (3,417,625) = ? Sep 23 09:22 UTC (GMT) factors (3,712,051) = ? Sep 23 09:22 UTC (GMT) common factors (divisors) (36,498; 49,770) = ? Sep 23 09:22 UTC (GMT) factors (8,815,006) = ? Sep 23 09:22 UTC (GMT) factors (43,550) = ? Sep 23 09:22 UTC (GMT) factors (1,222,556) = ? Sep 23 09:22 UTC (GMT) common factors (divisors) (32; 56) = ? Sep 23 09:22 UTC (GMT) common factors (divisors) (30,973; 15) = ? Sep 23 09:22 UTC (GMT) factors (14,968,098) = ? Sep 23 09:22 UTC (GMT) factors (38) = ? Sep 23 09:22 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;