710 − 510 is divisible by
11
Applied Concept:
(a2 − b2 ) = (a + b) (a − b)
Divisibility Rule of 11: If the difference between the sum of alternate digits of a number is divisible by 11, then the number is completely divisible by 11.
Calculation:
It is given that,
710 − 510
⇒ (75 + 55) (75 − 55)
⇒ 75 = 343 × 49 = 16807
⇒ 55 = 625 × 5 = 3125
⇒ 710 − 510 = 19932(75 − 55)
Now, for the number 19932 ,
Sum of odd-positioned digits = 2 + 9 + 1 = 12
Sum of even-positioned digits = 9 + 3 = 12
Therefore, the difference = 12 − 12 = 0
∴ The number is divisible by 11.
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