Factors and Multiples

A factor of a number is an exact divisor of that number. For example, 1, 2, 3 and 6 are exact divisors of 6. They are called the factors of 6.

Properties of Factors

  1. The number 1 is a factor of every number. For example 6 = 1 × 6, 18 = 1 × 18 and so on.
  2. Every number is a factor of itself. For example, You can write 7 as 7 = 7 × 1.
  3. Every factor of a number is an exact divisor of that number. For example, factors of 16 are 1, 2, 4, 8, 16.
  4. Every factor is less than or equal to the given number. For example, factors of 34 are 1, 2, 17 and 34 itself.
  5. Number of factors of a given number are finite. For example, the number 76 has 5 factors.

Properties of Multiples

  1. Every multiple of a number is greater than or equal to that number. For example, multiples of 7 are 7, 14, 21, 28,... 
  2. The number of multiples of a given number is infinite. For example, multiples of 5 are 5, 10, 15, 20,... The list is endless.
  3. Every number is a multiple of itself. For example, 7 = 7 × 1.

Perfect Numbers

A number for which sum of all its factors is equal to twice the number is called a perfect number. The numbers 6 and 28 are perfect numbers.

The factors of 6 are 1, 2, 3 and 6. Also, 1 + 2 + 3 + 6 = 12 = 2 × 6. The sum of the factors of 6 is twice the number 6.

All the factors of 28 are 1, 2, 4, 7, 14 and 28. Adding these, 1 + 2 + 4 + 7 + 14 + 28 = 56 = 2 × 28. The sum of the factors of 28 is equal to twice the number 28.

Common Factors and Common Multiples

Two numbers having only 1 as a common factor are called co-prime numbers. For example, 4 and 15 are co-prime numbers.