Question

find the greatest number that divides 74112 and 152 with leaving the remainders 2, 4, and 6

Answer 1

Step-by-step explanation:

numbers given - 74,112,152

remainders 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

HCF = 2×1=2

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