**Question:** 1: Use Euclid’s division algorithm to find the HCF of:

I. 135 and 225

Class | 10th |

Subject | Maths |

Chapter | Real Numbers |

Exercise | 1.1 |

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**Solution:**

135 and 225

As you can see, from the question 225 is greater than 135. Therefore, by Euclid’s division algorithm, we

have,

225 = 135 × 1 + 90

Now, remainder 90 ≠ 0, thus again using division lemma for 90, we get,

135 = 90 × 1 + 45

Again, 45 ≠ 0, repeating the above step for 45, we get,

90 = 45 × 2 + 0

The remainder is now zero, so our method stops here. Since, in the last step, the divisor is 45,

therefore, HCF (225,135) = HCF (135, 90) = HCF (90, 45) = 45.

Hence, the HCF of 225 and 135 is 45.