Highest Common Factor of 267, 462 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 267, 462 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 267, 462 is 3 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 267, 462 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 267, 462 is 3.
HCF(267, 462) = 3
HCF of 267, 462 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 267, 462 is 3.
Highest Common Factor of 267,462 is 3
Step 1: Since 462 > 267, we apply the division lemma to 462 and 267, to get
462 = 267 x 1 + 195
Step 2: Since the reminder 267 ≠ 0, we apply division lemma to 195 and 267, to get
267 = 195 x 1 + 72
Step 3: We consider the new divisor 195 and the new remainder 72, and apply the division lemma to get
195 = 72 x 2 + 51
We consider the new divisor 72 and the new remainder 51,and apply the division lemma to get
72 = 51 x 1 + 21
We consider the new divisor 51 and the new remainder 21,and apply the division lemma to get
51 = 21 x 2 + 9
We consider the new divisor 21 and the new remainder 9,and apply the division lemma to get
21 = 9 x 2 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 267 and 462 is 3
Notice that 3 = HCF(9,3) = HCF(21,9) = HCF(51,21) = HCF(72,51) = HCF(195,72) = HCF(267,195) = HCF(462,267) .
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Frequently Asked Questions on HCF of 267, 462 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 267, 462?
Answer: HCF of 267, 462 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 267, 462 using Euclid's Algorithm?
Answer: For arbitrary numbers 267, 462 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.