Highest Common Factor of 971, 262, 67 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 971, 262, 67 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 971, 262, 67 is 1 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 971, 262, 67 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 971, 262, 67 is 1.
HCF(971, 262, 67) = 1
HCF of 971, 262, 67 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 971, 262, 67 is 1.
Highest Common Factor of 971,262,67 is 1
Step 1: Since 971 > 262, we apply the division lemma to 971 and 262, to get
971 = 262 x 3 + 185
Step 2: Since the reminder 262 ≠ 0, we apply division lemma to 185 and 262, to get
262 = 185 x 1 + 77
Step 3: We consider the new divisor 185 and the new remainder 77, and apply the division lemma to get
185 = 77 x 2 + 31
We consider the new divisor 77 and the new remainder 31,and apply the division lemma to get
77 = 31 x 2 + 15
We consider the new divisor 31 and the new remainder 15,and apply the division lemma to get
31 = 15 x 2 + 1
We consider the new divisor 15 and the new remainder 1,and apply the division lemma to get
15 = 1 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 971 and 262 is 1
Notice that 1 = HCF(15,1) = HCF(31,15) = HCF(77,31) = HCF(185,77) = HCF(262,185) = HCF(971,262) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 67 > 1, we apply the division lemma to 67 and 1, to get
67 = 1 x 67 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 67 is 1
Notice that 1 = HCF(67,1) .
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Frequently Asked Questions on HCF of 971, 262, 67 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 971, 262, 67?
Answer: HCF of 971, 262, 67 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 971, 262, 67 using Euclid's Algorithm?
Answer: For arbitrary numbers 971, 262, 67 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.