Highest Common Factor of 976, 32718 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 976, 32718 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 976, 32718 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 976, 32718 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 976, 32718 is 2.
HCF(976, 32718) = 2
HCF of 976, 32718 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 976, 32718 is 2.
Highest Common Factor of 976,32718 is 2
Step 1: Since 32718 > 976, we apply the division lemma to 32718 and 976, to get
32718 = 976 x 33 + 510
Step 2: Since the reminder 976 ≠ 0, we apply division lemma to 510 and 976, to get
976 = 510 x 1 + 466
Step 3: We consider the new divisor 510 and the new remainder 466, and apply the division lemma to get
510 = 466 x 1 + 44
We consider the new divisor 466 and the new remainder 44,and apply the division lemma to get
466 = 44 x 10 + 26
We consider the new divisor 44 and the new remainder 26,and apply the division lemma to get
44 = 26 x 1 + 18
We consider the new divisor 26 and the new remainder 18,and apply the division lemma to get
26 = 18 x 1 + 8
We consider the new divisor 18 and the new remainder 8,and apply the division lemma to get
18 = 8 x 2 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 976 and 32718 is 2
Notice that 2 = HCF(8,2) = HCF(18,8) = HCF(26,18) = HCF(44,26) = HCF(466,44) = HCF(510,466) = HCF(976,510) = HCF(32718,976) .
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Frequently Asked Questions on HCF of 976, 32718 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 976, 32718?
Answer: HCF of 976, 32718 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 976, 32718 using Euclid's Algorithm?
Answer: For arbitrary numbers 976, 32718 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.