Use Euclid’s Division Algorithm to Find the HCF of 136, 170 and 255

Video Explanation

Watch the video below to understand the complete solution using Euclid’s division algorithm:

Solution

Question: Use Euclid’s division algorithm to find the HCF of 136, 170 and 255.

Step 1: Find the HCF of 170 and 136

Using Euclid’s division algorithm:

170 = 136 × 1 + 34

Since the remainder is not zero, apply the algorithm again.

136 = 34 × 4 + 0

Here, the remainder is zero.

∴ HCF (170, 136) = 34

Step 2: Find the HCF of 34 and 255

Applying Euclid’s division algorithm:

255 = 34 × 7 + 17

Since the remainder is not zero, apply the algorithm again.

34 = 17 × 2 + 0

Here, the remainder is zero.

∴ HCF (255, 34) = 17

Final Answer

∴ The HCF of 136, 170 and 255 is 17.

Conclusion

Thus, using Euclid’s division algorithm step by step, we find that the HCF of 136, 170 and 255 is 17. This method is simple and very useful for examination purposes.