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Question

Show that:

(i) 13353 is divisible by 8.

(ii) 353+273 is divisible by 62.

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Solution

(i) (133 - 53)

[Using identity (a3 - b3) = (a - b)(a2 + ab + b2)]

=(13 - 5)(132 + 13 × 5 + 52)

=8(169 + 65 + 25)

Therefore, the number is divisible by 8.

(ii) (353 + 273)

[Using identity (a3 + b3)=(a + b)(a2 - ab + b2)]

=(35 + 27)(352 + 35× 27 + 272)

=62 × (352 + 35 × 27 + 272)

Therefore, the number is divisible by 62.


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