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Sum

Show that 954 – 459 is exactly divisible by 99.

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#### Solution

**To show:** 954 – 459 is exactly divisible by 3 99, where a = 9, b = 5, c = 4

abc = 100a + 10b + c

⇒ 954 = 100 x 9 + 10 x 5 + 4

⇒ 954 = 900 + 50 + 4 ………(i)

and 459 = 100 x 4+ 10 x 5 + 9

⇒ 459 = 400 + 50 + 9 ……..(ii)

Subtracting (ii) from (i), we get

954 – 459 = 900 + 50 + 4 – 400 – 50 – 9

⇒ 954 – 459 = 500 – 5

⇒ 954 – 459 = 495

⇒ 954 – 459 = 99 x 5

Hence, 954 – 459 is exactly divisible by 99

Hence proved.

Concept: Some Interesting Properties

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