Highest Common Factor of 974, 62976 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 974, 62976 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 974, 62976 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 974, 62976 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 974, 62976 is 2.
HCF(974, 62976) = 2
HCF of 974, 62976 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 974, 62976 is 2.
Highest Common Factor of 974,62976 is 2
Step 1: Since 62976 > 974, we apply the division lemma to 62976 and 974, to get
62976 = 974 x 64 + 640
Step 2: Since the reminder 974 ≠ 0, we apply division lemma to 640 and 974, to get
974 = 640 x 1 + 334
Step 3: We consider the new divisor 640 and the new remainder 334, and apply the division lemma to get
640 = 334 x 1 + 306
We consider the new divisor 334 and the new remainder 306,and apply the division lemma to get
334 = 306 x 1 + 28
We consider the new divisor 306 and the new remainder 28,and apply the division lemma to get
306 = 28 x 10 + 26
We consider the new divisor 28 and the new remainder 26,and apply the division lemma to get
28 = 26 x 1 + 2
We consider the new divisor 26 and the new remainder 2,and apply the division lemma to get
26 = 2 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 974 and 62976 is 2
Notice that 2 = HCF(26,2) = HCF(28,26) = HCF(306,28) = HCF(334,306) = HCF(640,334) = HCF(974,640) = HCF(62976,974) .
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Frequently Asked Questions on HCF of 974, 62976 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 974, 62976?
Answer: HCF of 974, 62976 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 974, 62976 using Euclid's Algorithm?
Answer: For arbitrary numbers 974, 62976 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.