Find the largest number which divides 245 and 1029 leaving remainder 5 in each case.

Foundation

Mathematics Foundation

HCF and LCM

Question

Find the largest number which divides

245

and

1029

leaving remainder

5

in each case.

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It is given that the required number when divides

245

and

1029

, the remainder is

5

in each case, This means that

245 - 5 = 240

and

1029 - 5 = 1024

are completely divisible by the required number.

It follows from this that the required number is a common factor of

240

and

1024

. It is also given that the required number is the largest number satisfying the given property. Therefore, it is the

H C F

240

and

1024

Let us now find the

H C F

240

and

1024

by Prime factorization method(refer above image).
Clearly,

H C F

240

and

1024

is common divisor i.e.,

2 \times 2 \times 2 \times 2 = 16

.
Hence, required number

= 16