Divisibility Rules: Test for 3,27,087

We need to find which number among the options (3, 12, 8, 5) divides 3,27,087. We use divisibility rules.

Checking Divisibility by 3

Rule: A number is divisible by 3 if the sum of its digits is divisible by 3.

• Sum of digits of 3,27,087 = 3 + 2 + 7 + 0 + 8 + 7 = 27.
• Check: Is 27 divisible by 3? Yes, \(27 \div 3 = 9\).
• Result: 3,27,087 is divisible by 3.

Checking Divisibility by 12

Rule: A number is divisible by 12 if it's divisible by both 3 and 4.

• We already know 3,27,087 is divisible by 3.
• Check divisibility by 4: A number is divisible by 4 if the number formed by its last two digits is divisible by 4.
• Last two digits are 87.
• Check: Is 87 divisible by 4? No, \(87 \div 4 = 21\) with a remainder of 3.
• Result: 3,27,087 is not divisible by 4, hence not divisible by 12.

Checking Divisibility by 8

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

• Last three digits are 087.
• Check: Is 87 divisible by 8? No, \(87 \div 8 = 10\) with a remainder of 7.
• Result: 3,27,087 is not divisible by 8.

Checking Divisibility by 5

Rule: A number is divisible by 5 if its last digit is 0 or 5.

• The last digit of 3,27,087 is 7.
• Result: 3,27,087 is not divisible by 5.

Final Answer

Only the number 3 satisfies the divisibility test for 3,27,087.