Question

Find the number which divides 200 and 136 leaving 8 as remainder.

Answer 1

Two ways to find.
1. Find n Natural numbers that 136/n gives reminder 8. and check with 200. Bad Way.
2. Logic way. ... Find Greatest common divisor of 200+8 and 136+8. GCD(208;144)=(64;144)=(64;80)=(64;16). 64 is divisible by 16 so 16 is the answer . check 200/16 reminder 8 so 136/8

Answer 2

Answer:16,32,64

Explanation:

Given no divides 200 and 136 leaving remainder 8

Let no. be P

therefore

200=kP+8

where k is any constant

136=aP+8

where a is another constant

subtracting

64=P(k-a)

i.e.P is multiple of 64

either 64,32,16

but not 8,4,2 as they completely divide both numbers