Find the least number which leaves 3 as remainder when divided by 8, 1

1.	Find the least number which leaves 3 as remainder when divided by 8, 12and 16.
Answer» Answer :- To find the Least number X, X should leave a remainder 3 when divided by 16 , 12, 8. X Should completely divisible by 7. So, Let's start with 16 because we can reach X quickly [ 16 is big number and we are MOVING 16 steps everytime] Given CONDITION, X % 16 = 3 If a number X when divided by 16 gives some remainder Y then same number when divided by 8 gives the same remainder Y because 8 is a multiple of 16. So need not bother about 8. Now coming to number 12 with 16, 3 * 2 * 2 = 12 vs 2 * 2 * 2 * 2 = 16 12 is a contains multiple 3 where 16 does not contain the same. So X-3 should be a multiple of 3. Now X can be 51(48+3), 99(96+3), 147(144+3)…… (Choose multiples of 48 (16*3)) Now let’s search for numbers divisible by 7 in the above list. 147 is one such number and least number. Answer = 147

Find the least number which leaves 3 as remainder when divided by 8, 12and 16.

Answer»

To find the Least number X,

X should leave a remainder 3 when divided by 16 , 12, 8.

X Should completely divisible by 7.

So, Let's start with 16 because we can reach X quickly [ 16 is big number and we are MOVING 16 steps everytime]

X % 16 = 3

If a number X when divided by 16 gives some remainder Y then same number when divided by 8 gives the same remainder Y because 8 is a multiple of 16.

So need not bother about 8.

Now coming to number 12 with 16,

3 * 2 * 2 = 12 vs 2 * 2 * 2 * 2 = 16

12 is a contains multiple 3 where 16 does not contain the same.

So X-3 should be a multiple of 3.

Now X can be

51(48+3), 99(96+3), 147(144+3)…… (Choose multiples of 48 (16*3))

Now let’s search for numbers divisible by 7 in the above list.

147 is one such number and least number.

Answer = 147