Question

Find the largest no. WhIch when divided by 245 and 1029 leaves remainder 5 in each case

Answer 1

If I avoid the remainders, it seems like the number is divisible by (245–5=240)(245–5=240) and (1029–5=1024)(1029–5=1024). Its something like this: we know 5×1=5,5×2=105×1=5,5×2=10. The number 1010 doesn’t go into 55 and leaves a remainder of 55 if we try to divide.The largest number, hmm? Aren’t we looking for the HCF

1024240=210=24×3×51024=210240=24×3×5

HCF(1024,240)=24=16

Answer 2

in this case we have to find the LHS of two numbers
LHS of 245 & 1029
49*5 & 49*21
so LHS is 49*21*5=5145
so we need 5 remainder in each case so add 5 to 5145 so answer is 5150