Find the greatest number that can divide 166 and 237 leaving remainders 5 and 7 represtively
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Let the number be a
When we divide 166 by a it leaves remainder as 5 means the perfect number that 'a' divides is 5 less than 166 i.e. if we subtract 5 from 166 we'll get a number which is completely divisible by a.
Similarly, if we subtract 7 from 237 we'll get a number which is completely divisible by a.
so numbers which are completely divisible by a are 161 and 230
a will be the highest common factor of 161 and 230 which is 23.
Hence, the required number is 23
When we divide 166 by a it leaves remainder as 5 means the perfect number that 'a' divides is 5 less than 166 i.e. if we subtract 5 from 166 we'll get a number which is completely divisible by a.
Similarly, if we subtract 7 from 237 we'll get a number which is completely divisible by a.
so numbers which are completely divisible by a are 161 and 230
a will be the highest common factor of 161 and 230 which is 23.
Hence, the required number is 23
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