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# The number ab - ba where a and b are digits and a > b is divisible by ________.

**Solution:**

If ab is written in the generalised form we get

ab = 10a + b

If ba is written in the generalised form we have

ba = 10b + a

Therefore

ab - ba = 10a + b - (10b + a) = 9a - 9b = 9(a - b)

Therefore the number ab - ba is divisible by 9.

**✦ Try This: **The number abc - cba where a and b are digits and a - b is divisible by ________.

If abc is written in generalised form we have:

abc = 100a + 10b + c - (100c + 10b + a) = 99a - 99c = 99(c - a)

Therefore abc - cba is divisible by 99

**☛ Also Check: **NCERT Solutions for Class 8 Maths Chapter 16

**NCERT Exemplar Class 8 Maths Chapter 13 Sample Problem 5**

## The number ab - ba where a and b are digits and a > b is divisible by ________.

**Summary:**

The number ab - ba where a and b are digits and a > b is divisible by 9.

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