A number when divided by 80 leaves remainder 20. What is the remainder when…

Concept

When a number leaves a remainder on division, write it as: N = (divisor x quotient) + remainder. A key rule of divisibility: if the first divisor D is itself a multiple of a smaller divisor d (so D = d x m), then every multiple of D is also a multiple of d. So when you divide N by d, the (divisor x quotient) part vanishes and the remainder of N by d equals just the remainder-part reduced modulo d.

Application

1. Translate the condition. Dividing by 80 leaves remainder 20, so the number has the form N = 80k + 20, where k is the whole-number quotient.

2. Compare the two divisors. The new divisor is 16, and 80 = 16 x 5. So 80k = 16 x 5k is an exact multiple of 16 and contributes remainder 0.

3. Reduce only the leftover part. So N divided by 16 has the same remainder as 20 divided by 16. Now 20 = 16 x 1 + 4.

4. Read off the remainder: it is 4.

Cross-check

Pick any concrete value of k and test directly:

• k = 1 gives N = 100; 100 = 16 x 6 + 4, remainder 4.

• k = 2 gives N = 180; 180 = 16 x 11 + 4, remainder 4.

The remainder is the same for every choice of k, confirming the result 4.