Highest Common Factor of 8718, 9616 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 8718, 9616 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 8718, 9616 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 8718, 9616 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 8718, 9616 is 2.
HCF(8718, 9616) = 2
HCF of 8718, 9616 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8718, 9616 is 2.
Highest Common Factor of 8718,9616 is 2
Step 1: Since 9616 > 8718, we apply the division lemma to 9616 and 8718, to get
9616 = 8718 x 1 + 898
Step 2: Since the reminder 8718 ≠ 0, we apply division lemma to 898 and 8718, to get
8718 = 898 x 9 + 636
Step 3: We consider the new divisor 898 and the new remainder 636, and apply the division lemma to get
898 = 636 x 1 + 262
We consider the new divisor 636 and the new remainder 262,and apply the division lemma to get
636 = 262 x 2 + 112
We consider the new divisor 262 and the new remainder 112,and apply the division lemma to get
262 = 112 x 2 + 38
We consider the new divisor 112 and the new remainder 38,and apply the division lemma to get
112 = 38 x 2 + 36
We consider the new divisor 38 and the new remainder 36,and apply the division lemma to get
38 = 36 x 1 + 2
We consider the new divisor 36 and the new remainder 2,and apply the division lemma to get
36 = 2 x 18 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8718 and 9616 is 2
Notice that 2 = HCF(36,2) = HCF(38,36) = HCF(112,38) = HCF(262,112) = HCF(636,262) = HCF(898,636) = HCF(8718,898) = HCF(9616,8718) .
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Frequently Asked Questions on HCF of 8718, 9616 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 8718, 9616?
Answer: HCF of 8718, 9616 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8718, 9616 using Euclid's Algorithm?
Answer: For arbitrary numbers 8718, 9616 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.