21,300: Calculate all the factors (divisors) of the number (proper, improper and the prime factors)

The factors (divisors) of the number 21,300

21,300 is a composite number and can be prime factorized. So what are all the factors (divisors) of the number 21,300?

A factor (a divisor) of the number 21,300 is a natural number B which when multiplied by another natural number C equals the given number 21,300. Both B and C are factors of 21,300.


To find all the factors (divisors) of the number 21,300:
- break down the number into prime factors (number's prime factorization),
- then multiply these prime factors in all their unique combinations, that give different results.



The prime factorization:

The prime factorization of the number 21,300 = dividing the number 21,300 into smaller, prime numbers. The number 21,300 results from the multiplication of these prime numbers.


21,300 = 22 × 3 × 52 × 71
21,300 is not a prime number but a composite one.


* The natural numbers that are only divisible by 1 and themselves are called prime numbers. A prime number has exactly two factors: 1 and the number itself.
* A composite number is a natural number that has at least one other factor than 1 and itself.




How do I find all the factors (divisors) of the number?

21,300 = 22 × 3 × 52 × 71


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
2 × 5 = 10
22 × 3 = 12
3 × 5 = 15
22 × 5 = 20
52 = 25
2 × 3 × 5 = 30
2 × 52 = 50
22 × 3 × 5 = 60
prime factor = 71
3 × 52 = 75
22 × 52 = 100
2 × 71 = 142
This list continues below...

... This list continues from above
2 × 3 × 52 = 150
3 × 71 = 213
22 × 71 = 284
22 × 3 × 52 = 300
5 × 71 = 355
2 × 3 × 71 = 426
2 × 5 × 71 = 710
22 × 3 × 71 = 852
3 × 5 × 71 = 1,065
22 × 5 × 71 = 1,420
52 × 71 = 1,775
2 × 3 × 5 × 71 = 2,130
2 × 52 × 71 = 3,550
22 × 3 × 5 × 71 = 4,260
3 × 52 × 71 = 5,325
22 × 52 × 71 = 7,100
2 × 3 × 52 × 71 = 10,650
22 × 3 × 52 × 71 = 21,300

The final answer:
(scroll down)

21,300 has 36 factors (divisors):
1; 2; 3; 4; 5; 6; 10; 12; 15; 20; 25; 30; 50; 60; 71; 75; 100; 142; 150; 213; 284; 300; 355; 426; 710; 852; 1,065; 1,420; 1,775; 2,130; 3,550; 4,260; 5,325; 7,100; 10,650 and 21,300
out of which 4 prime factors: 2; 3; 5 and 71
21,300 and 1 are called by some authors improper factors (improper divisors), 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.


The latest 5 sets of calculated factors (divisors): of one number or the common factors of two numbers

The factors (divisors) of 21,300 = ? Nov 28 11:51 UTC (GMT)
The factors (divisors) of 428,158 = ? Nov 28 11:51 UTC (GMT)
The common factors (divisors) of 897,017,143 and 0 = ? Nov 28 11:51 UTC (GMT)
The factors (divisors) of 8,051,472 = ? Nov 28 11:51 UTC (GMT)
The common factors (divisors) of 842,772 and 0 = ? Nov 28 11:51 UTC (GMT)
The list of all the calculated factors (divisors) of one or two numbers

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.

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

Some articles on the prime numbers

What is a prime number? Definition, examples

What is a composite number? Definition, examples

The prime numbers up to 1,000

The prime numbers up to 10,000

The Sieve of Eratosthenes

The Euclidean Algorithm

Completely reduce (simplify) fractions to the lowest terms: Steps and Examples