Question

Using division algorithm and find the largest number which divides 147 and 234 the remainder obtained 12 and 9 respectively

Answer 1

If 969 is divided and leaves a remainder 9 then the number which it exactly divides is 960

if 2059 is divided and leaves a remainder 11 then the number which it exactly divides is 2048

now let us find it's hcf

2048 = 960 × 2 +128

960 = 128 × 7 + 64

128 = 64 × 2 + 0

therefore the largest number that divides 969 and 2059 to leave remainder 9 and 11 respectively is 64.