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Question

Find the largest number which divides 70 and125 leaves remainders 5 and 8 respectively.


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Solution

Solve for the HCF of the given numbers

The largest number which divides 70 and125, leaving remainders 5 and 8 respectively.

70-5=65125-5=120

H.C.F of 65 and 117 will be given as,

Factors of 65=1,5,13,65

Factors of 117=1,3,9,13,39,117

Common Factors =1,13

Highest Common factor =13

Hence, the largest number that divides70 and125, leaving remainders5 and 8, respectively is 13.


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