5: All the proper, improper and prime factors (divisors) of number

5 has 2 factors: 1 and 5.
5 (some consider that 1 too) is an improper factor (divisor).

How to factor a number, how to break it down to prime factors (prime factorization)

5 is a prime number, it cannot be broken down to other prime factors.
Positive integers that are only dividing by themselves and 1 are called prime numbers.

4 = ? ... 6 = ?

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

Latest calculated (found) factors (divisors)

factors (5) = ? Mar 31 13:49 UTC (GMT)
factors (604,453) = ? Mar 31 13:49 UTC (GMT)
factors (815,730,721) = ? Mar 31 13:49 UTC (GMT)
factors (63) = ? Mar 31 13:49 UTC (GMT)
common factors (divisors) (25; 100) = ?Mar 31 13:49 UTC (GMT)
factors (48) = ? Mar 31 13:49 UTC (GMT)
common factors (divisors) (1,080; 720) = ?Mar 31 13:49 UTC (GMT)
factors (9,600) = ? Mar 31 13:49 UTC (GMT)
factors (18) = ? Mar 31 13:49 UTC (GMT)
factors (6,672) = ? Mar 31 13:49 UTC (GMT)
factors (159,375) = ? Mar 31 13:49 UTC (GMT)
factors (3,397) = ? Mar 31 13:49 UTC (GMT)
factors (410) = ? Mar 31 13:49 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