Question
Use Euclid's division algorithm to find the HCF of:
136, 170 and 255
136, 170 and 255
✓
Answer
Given integers are 136, 170 and 255.
Let us first find the HCF of 136, 170 by Euclid lemma.
Clearly, 170 > 136. So, we will apply Euclid’s division lemma to 136 and 170.
170 = 136 × 1 + 34
Remainder is 34 which is a non-zero number.
Now, apply Euclid’s division lemma to 136 and 34.
136 = 34 × 4 + 0
The remainder at this stage is zero.
Therefore, 34 is the HCF of 136 and 170.
Now, again use Euclid’s division lemma to find the HCF of 34 and 255.
255 = 34 × 7 + 17
Remainder is 17 which is a non-zero number.
Now, apply Euclid’s division lemma to 34 and 17.
34 = 17 × 2 + 0
The remainder at this stage is zero.
Therefore, 17 is the HCF of 136, 170 and 255.
Let us first find the HCF of 136, 170 by Euclid lemma.
Clearly, 170 > 136. So, we will apply Euclid’s division lemma to 136 and 170.
170 = 136 × 1 + 34
Remainder is 34 which is a non-zero number.
Now, apply Euclid’s division lemma to 136 and 34.
136 = 34 × 4 + 0
The remainder at this stage is zero.
Therefore, 34 is the HCF of 136 and 170.
Now, again use Euclid’s division lemma to find the HCF of 34 and 255.
255 = 34 × 7 + 17
Remainder is 17 which is a non-zero number.
Now, apply Euclid’s division lemma to 34 and 17.
34 = 17 × 2 + 0
The remainder at this stage is zero.
Therefore, 17 is the HCF of 136, 170 and 255.
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