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Now, let’s divide 12 by 4, 5 and 6.

3 2 2
4 12 5 12 6 12
– 12 – 10 – 12
0 2 0
Observe that 4 and 6 divide 12 completely without leaving any remainder. But, 12 ÷ 5 leaves a
remainder 2.

Thus, we can say that a factor of a number is an exact divisor of that number. In other words, if a
number divides another number exactly, that is, without leaving any remainder, then the smaller
number is a factor of the bigger number.

Also, note that the bigger number is the multiple of the smaller number. That means the multiple
of a number is always divisible by its factors.

Multiples of a number can be obtained by multiplying the number with counting numbers 1,
2, 3, 4, …

Difference between Factors and Multiples

Factors Multiples
It is the exact divisor of the given number. When a number is multiplied by other numbers,
multiples are obtained.

Number of factors of a given number are finite. Number of multiples of a given number are infinite.
Factors are less than or equal to the given number. Multiples are greater than or equal to the given
number.

To find the factor of a number, division is used. In order to get the multiple of a number,
multiplication is used.
Every number is the greatest factor of itself. Every number is the smallest multiple of itself.

Example 1: Write all the factors of 56.

Solution: We know that
Quick Check
1 × 56 = 56
Fill in the blanks with the missing factors.
2 × 28 = 56
1. 8 × .......... = 32 2. 5 × .......... = 40
4 × 14 = 56 3. .......... × 6 = 24 4. .......... × 5 = 60
7 × 8 = 56

Thus, 1, 2, 4, 7, 8, 14, 28 and 56 are the factors of 56.

Example 2: Write the first five multiples of 17.
Solution: Let us multiply 17 by first five counting numbers.

17 × 1 = 17; 17 × 2 = 34; 17 × 3 = 51; 17 × 4 = 68 and 17 × 5 = 85

Hence, the products 17, 34, 51, 68 and 85 are the first five multiples of 17.

139 Prime Time