Question

A six-digit number is formed by repeating a three-digit number. For example 256256, 678678, etc. Any number of this form is divisible by ______.

विकल्प

• 7 only

• 11 only

• 13 only

• 1001

Answer 1

A six-digit number is formed by repeating a three-digit number. For example 256256, 678678, etc. Any number of this form is divisible by 1001.

Explanation:

Let the six-digit number be abcabc, then

= 100000 × a + 10000b + 1000c + 100a + 10b + c

= a(100000 + 100) + b(10000 + 10) + c(1000 + 1)

= a(100100) + b(10010) + c(1001)

= 1001(a × 100 + b × 10 + c)

Hence, it is divisible by 1001.