Question

Find the greatest number that will divide 114,143 and 172 leaving remainders 2,3 and 4 respectively (with explanation)

Answer 1

Answer:

114-2= 112, 143-3=140 and 172-4= 168 are the required numbers.

Using Prime Factorization method,

112 = 2×2×2×2×7

140 = 2×2×5×7

168 = 2×2×2×3×7

H.C.F.(112,140,172) = 2×2×7=28

Therefore, 28 is the greatest number which will divide 114,143 and 172 by leaving remainder 2,3 and 4 .

Hope this helps you.