Q12 of 56 Page 17

Find the largest number that divides 220, 313 and 716 leaving remainder 3 in each case?

On dividing by 220, 313 and 716 remainder is 3

⇒ 220 – 3 = 217


Also 313 – 3 = 310


And 716 – 3 = 713


By prime factorizing of 217, 310 and 713 we get


217 = 7 × 31


310 = 2 × 5 × 31


713 = 23 × 31


so, the H.C.F of 217,310 and 713 = 31


Hence the largest number that divides 220, 313 and 716, leaving a remainder 3 in each case is 31.


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