Highest Common Factor of 6961, 9612 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 6961, 9612 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 6961, 9612 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 6961, 9612 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 6961, 9612 is 1.
HCF(6961, 9612) = 1
HCF of 6961, 9612 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6961, 9612 is 1.
Highest Common Factor of 6961,9612 is 1
Step 1: Since 9612 > 6961, we apply the division lemma to 9612 and 6961, to get
9612 = 6961 x 1 + 2651
Step 2: Since the reminder 6961 ≠ 0, we apply division lemma to 2651 and 6961, to get
6961 = 2651 x 2 + 1659
Step 3: We consider the new divisor 2651 and the new remainder 1659, and apply the division lemma to get
2651 = 1659 x 1 + 992
We consider the new divisor 1659 and the new remainder 992,and apply the division lemma to get
1659 = 992 x 1 + 667
We consider the new divisor 992 and the new remainder 667,and apply the division lemma to get
992 = 667 x 1 + 325
We consider the new divisor 667 and the new remainder 325,and apply the division lemma to get
667 = 325 x 2 + 17
We consider the new divisor 325 and the new remainder 17,and apply the division lemma to get
325 = 17 x 19 + 2
We consider the new divisor 17 and the new remainder 2,and apply the division lemma to get
17 = 2 x 8 + 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 6961 and 9612 is 1
Notice that 1 = HCF(2,1) = HCF(17,2) = HCF(325,17) = HCF(667,325) = HCF(992,667) = HCF(1659,992) = HCF(2651,1659) = HCF(6961,2651) = HCF(9612,6961) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 6961, 9612 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 6961, 9612?
Answer: HCF of 6961, 9612 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6961, 9612 using Euclid's Algorithm?
Answer: For arbitrary numbers 6961, 9612 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.