Find the HCF of 1288 and 575 and Express it as a Linear Combination

Video Explanation

Watch the video below to understand the complete solution step by step:

Solution

Question: Find the HCF of the following pairs of integers and express it as a linear combination of them:

1288 and 575

Step 1: Use Euclid’s Division Algorithm

1288 = 575 × 2 + 138

575 = 138 × 4 + 23

138 = 23 × 6 + 0

Since the remainder is zero,

∴ HCF (1288, 575) = 23

Step 2: Express HCF as a Linear Combination

23 = 575 − 138 × 4

23 = 575 − 4 × (1288 − 575 × 2)

23 = 575 − 4 × 1288 + 8 × 575

23 = 9 × 575 − 4 × 1288

Final Answer

∴ The HCF of 1288 and 575 is 23 and it can be expressed as:

23 = 9 × 575 − 4 × 1288

Conclusion

Thus, using Euclid’s division algorithm, we found the HCF of 1288 and 575 and expressed it as a linear combination of the given integers.