Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 10th

Use Euclid’s Division Algorithm to find the Highest Common Factor (H.C.F) of 340 and 412 - Mathematics

Sum

Use Euclid’s Division Algorithm to find the Highest Common Factor (H.C.F) of 340 and 412

Solution

To find the H.C.F. of 340 and 412. Using Euclid’s division algorithm.

We get 412 = 340 × 1 + 72

The remainder 72 ≠ 0

Again applying Euclid’s division algorithm

340 = 72 × 4 + 52

The remainder 52 ≠ 0.

Again applying Euclid’s division algorithm

72 = 52 × 1 + 20

The remainder 20 ≠ 0.

Again applying Euclid’s division algorithm,

52 = 20 × 2 + 12

The remainder 12 ≠ 0.

Again applying Euclid’s division algorithm.

20 = 12 × 1 + 8

The remainder 8 ≠ 0.

Again applying Euclid’s division algorithm

12 = 8 × 1 + 4

The remainder 4 ≠ 0.

Again applying Euclid’s division algorithm

8 = 4 × 2 + 0

The remainder is zero.

Therefore H.C.F. of 340 and 412 is 4.

Concept: Euclid’s Division Algorithm
Is there an error in this question or solution?