Question

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

Answer 1

245 and 1029 are the given two numbers,
If they leave remainder 5 , when they are divided by some number.
so remove 5 from both the number,
We get 240 and 1024,
find the G.C.D of both the number
we get 16 as the G.C.D
240 = (2×2×2×2)×3×5
1024 = (2×2×2×2)×2×2×2×2×2×2
G.C.D = 16
Therefore the greatest number that divides 245 and 1029 and leaves the remainder 5 is 16

Answer 2

Hi
Required number = 245-5 = 240 and 1029-5 = 1024
hcf of 240 and 1024

240 = 2×2×2×2×3×5
1024 = 2×2×2×2×2×2×2×2×2×2.

hcf of 240 and 1024 = 2×2×2×2 = 16
16 is the largest number which divides 245 and 1029 leaving remainder 5 in each case

thank you