Question

2. When a number is divided by 12, the quotient is 136 and the remainder is 10. What is the number?​

Answer 1

Answer:

Let's call that number “n”. When a number divided by “m” and give us “k” and the remainder is “r” (m, n ,k , r is in N; m ≠ 0), you can write “n” as:

n = m × k + r;

Apply this for m = 36 and r = 19

n = 36 × k + 19; (k, n in N)

= 12 × 3 × k +12 + 7

= 12 × (3 × k + 1) + 7

As you see, (3 × k + 1) is now the new “k”, let's call it “k'” and re-write n:

n = 12 × k' + 7

Now, you can see that “r” is 7. So the remainder is 7.