Question

find the greatest number which divides 74, 112, 152 leaving the remainder 2, 4, 6 respectively

Answer 1

Step-by-step explanation:

Numbers given - 74 , 112 , 152

remainder- 2, 4, 6 respectively.

So if we subtract the reminder from the given number so we get the exact number.

So 74-2=72

112-4=108

152-6=146

So here we get the exact number. Now we have to find the greatest number which divides 74 , 112, 152= HCF Of 72, 108, 146

HCF of 72 , 108 , 146 =

prime factorisation of 72= 2×2×2×3×3

". " " ". " " 108=2×2×3×3×3

". ". ". ". ". ". 146= 2×73

H.C.F = 2×1=2

So 2 is the greatest number which divides 74, 112 , 154 leaving remainder 2 , 4 , 6 respectively..

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