Which of the following number is not divisible by 72?

Correct Answer: 95142

Explanation:

To determine which number is not divisible by 72, we can use the divisibility rules for the prime factors of 72.

First, break down 72 into its co-prime factors:

$72=8\times 9$

A number is divisible by 72 if and only if it is divisible by both 8 and 9.

1. Divisibility Rule for 8:
A number is divisible by 8 if the number formed by its last three digits is divisible by 8.

2. Divisibility Rule for 9:
A number is divisible by 9 if the sum of all its digits is divisible by 9.

Let's check the given options:

Option 1: 95112
• Last three digits: 112
112 ÷ 8 = 14 (Divisible by 8)
• Sum of digits: 9 + 5 + 1 + 1 + 2 = 18
18 ÷ 9 = 2 (Divisible by 9)
Since 95112 is divisible by both 8 and 9, it is divisible by 72.

Option 2: 95142
• Last three digits: 142
142 ÷ 8 = 17.75 (Not divisible by 8)
• Sum of digits: 9 + 5 + 1 + 4 + 2 = 21
21 ÷ 9 = 2.33 (Not divisible by 9)
Since 95142 is not divisible by 8 or 9, it is not divisible by 72.

Option 3: 88848
• Last three digits: 848
848 ÷ 8 = 106 (Divisible by 8)
• Sum of digits: 8 + 8 + 8 + 4 + 8 = 36
36 ÷ 9 = 4 (Divisible by 9)
Since 88848 is divisible by both 8 and 9, it is divisible by 72.

Option 4: 88704
• Last three digits: 704
704 ÷ 8 = 88 (Divisible by 8)
• Sum of digits: 8 + 8 + 7 + 0 + 4 = 27
27 ÷ 9 = 3 (Divisible by 9)
Since 88704 is divisible by both 8 and 9, it is divisible by 72.

Thus, 95142 is the number that is not divisible by 72.