Question

The greatest number that will divide 162, 257 and 324 leaving remainder 6, 10 and 12 respectively is

A) 13
B) 12
C) 17
D) 11

Please explain in detail...

Answer 1

162-6=156
257-10=247
324-12=312
Now take HCF of 156 , 312 ,247 = 13.
Therefore greatest number that will divide 162,257,324 leaving remainder 6, 10 & 12 is 13

Answer 2

Concept

The HCF (Highest Common Factor) of numbers is the highest number among all the common factors of the given numbers.

For example, the HCF of 12 and 48 is 12 because 12 is the highest common factor of 12 and 48.

Find

The greatest number that will divide 162, 257 and 324 leaving remainder 6, 10 and 12 respectively

Solution

After dividing 162 leaves a remainder 6 means

= 162-6 = 156

Similarly

257 - 10 = 247

324 - 12 = 312

Calculating HCF of 156, 247, 312

HCF (156, 247, 312) = 13

The greatest number that will divide 162, 257 and 324 leaving remainder 6, 10 and 12 respectively is 13

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