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Use Euclid’s division algorithm to find the HCF of: 867 and 225

Sachin Khanna by Sachin Khanna
May 31, 2020
in NCERT Question Solutions
0

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
Previous Question Use Euclid’s division algorithm to find the HCF of: III. 196 and 38220
Next Question Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.

Solution:

READ ALSO

Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m, 9m + 1 or 9m + 8.

Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m.

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.

Next Post

Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.

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