HOW MANY 3 DIGIT NUMBERS ARE DIVISIBLE BY 6 IN ALL ?

Key Concept

Let us consider the first 'n' natural numbers.

1, 2, 3, ........... n

If you want to find the number of numbers which are divisible by 6 in the first natural numbers, you have to divide 'n' by 6.

Let n/6 = k.

If 'k' is an integer, then the number of numbers which are divisible by 6 in the first 'n' natural numbers is 'k'.

If 'k' is a decimal number, then the number of numbers which are divisible by 6 in the first 'n' natural numbers is the largest integer contained in 'k'.

Consider the following example to understand the above concept.

Find the number of numbers which are divisible by 6 in the first 100 natural numbers.

Divide 100 by 6.

100 ÷ 6 ≈ 16.67

The quotient of (100 ÷ 6) is about 16.67 which is a decimal number. Don't round 16.67 to the next integer 17.

The largest integer contained in 16.67 is 16.

Therefore, the number of numbers which are divisible by 6 in the first 100 natural numbers is 16.

6, 12, 18, 24, 30, 36, 42, 48,

54, 60, 66, 72, 78, 84, 90, 96

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