Highest Common Factor of 364, 637, 71 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 364, 637, 71 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 364, 637, 71 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 364, 637, 71 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 364, 637, 71 is 1.
HCF(364, 637, 71) = 1
HCF of 364, 637, 71 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 364, 637, 71 is 1.
Highest Common Factor of 364,637,71 is 1
Step 1: Since 637 > 364, we apply the division lemma to 637 and 364, to get
637 = 364 x 1 + 273
Step 2: Since the reminder 364 ≠ 0, we apply division lemma to 273 and 364, to get
364 = 273 x 1 + 91
Step 3: We consider the new divisor 273 and the new remainder 91, and apply the division lemma to get
273 = 91 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 91, the HCF of 364 and 637 is 91
Notice that 91 = HCF(273,91) = HCF(364,273) = HCF(637,364) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 91 > 71, we apply the division lemma to 91 and 71, to get
91 = 71 x 1 + 20
Step 2: Since the reminder 71 ≠ 0, we apply division lemma to 20 and 71, to get
71 = 20 x 3 + 11
Step 3: We consider the new divisor 20 and the new remainder 11, and apply the division lemma to get
20 = 11 x 1 + 9
We consider the new divisor 11 and the new remainder 9,and apply the division lemma to get
11 = 9 x 1 + 2
We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get
9 = 2 x 4 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 91 and 71 is 1
Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(11,9) = HCF(20,11) = HCF(71,20) = HCF(91,71) .
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Frequently Asked Questions on HCF of 364, 637, 71 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 364, 637, 71?
Answer: HCF of 364, 637, 71 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 364, 637, 71 using Euclid's Algorithm?
Answer: For arbitrary numbers 364, 637, 71 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.