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

Given: - 245 and 1029 are numbers to be divided by some number that leaves 5 as the remainder

Let that some number i.e divisor is x

Since when x divides 245 and 1029 leaves remainder 5

Then, to completely divides them it should be reduced by 5

Therefore 245 – 5 = 240 and 1029 – 5 = 1024
Now as x divides both the number (i.e 240 and 1024) therefore

we have to find a highest common factor of 240 and 1024

Hence,

Factors of 240 = 2 x 2 x 2 x 2 x 3 x 5
Factors of 1024 =
Highest common factors are =
x = 16

So 16 is the number which divides both 249 and 1029 with 5 as remainder.