use Euclid's algorithm to find the HCF of 867 and 255
Answers
By Euclid's division algorithm,
a = bq + r
Now, HCF (867 and 255)
=> 867 = 255 × 3 + 102
=> 255 = 102 × 2 + 51
=> 102 = 51 × 2 +0
Therefore, HCF (867 and 255) = 51
Answer:
51 is the H.C.F of 867 and 255.
Step-by-step explanation:
⇒ Euclid's algorithm :
- c = dq + r
⇒ Where :
- c, d = integers
- q, r = quotient, remainder
⇒ Here, 867 and 255 are the integers, we have 867 > 255, so apply the division lemma to 867 and 255.
255 | 867 | 3
| 765
| 102
∴ 867 = 255 × 3 + 102
Since the remainder 102 ≠ 0, apply the division lemma to 255 and 102.
102 | 255 | 2
| 204
| 51
∴ 255 = 102 × 2 + 51
Since the remainder 51 ≠ 0, apply the division lemma to 102 and 51.
51 | 102 | 2
| 102
| 0
∴ 102 = 51 × 2 + 0
Since the remainder = 0, Euclid division lemma can be stopped and the H.C.F of 867 and 255 is 51.
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