Highest Common Factor of 638, 972 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 638, 972 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 638, 972 is 2 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 638, 972 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 638, 972 is 2.
HCF(638, 972) = 2
HCF of 638, 972 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 638, 972 is 2.
Highest Common Factor of 638,972 is 2
Step 1: Since 972 > 638, we apply the division lemma to 972 and 638, to get
972 = 638 x 1 + 334
Step 2: Since the reminder 638 ≠ 0, we apply division lemma to 334 and 638, to get
638 = 334 x 1 + 304
Step 3: We consider the new divisor 334 and the new remainder 304, and apply the division lemma to get
334 = 304 x 1 + 30
We consider the new divisor 304 and the new remainder 30,and apply the division lemma to get
304 = 30 x 10 + 4
We consider the new divisor 30 and the new remainder 4,and apply the division lemma to get
30 = 4 x 7 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 638 and 972 is 2
Notice that 2 = HCF(4,2) = HCF(30,4) = HCF(304,30) = HCF(334,304) = HCF(638,334) = HCF(972,638) .
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Frequently Asked Questions on HCF of 638, 972 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 638, 972?
Answer: HCF of 638, 972 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 638, 972 using Euclid's Algorithm?
Answer: For arbitrary numbers 638, 972 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.