Highest Common Factor of 9766, 5970 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 9766, 5970 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 9766, 5970 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 9766, 5970 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 9766, 5970 is 2.
HCF(9766, 5970) = 2
HCF of 9766, 5970 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9766, 5970 is 2.
Highest Common Factor of 9766,5970 is 2
Step 1: Since 9766 > 5970, we apply the division lemma to 9766 and 5970, to get
9766 = 5970 x 1 + 3796
Step 2: Since the reminder 5970 ≠ 0, we apply division lemma to 3796 and 5970, to get
5970 = 3796 x 1 + 2174
Step 3: We consider the new divisor 3796 and the new remainder 2174, and apply the division lemma to get
3796 = 2174 x 1 + 1622
We consider the new divisor 2174 and the new remainder 1622,and apply the division lemma to get
2174 = 1622 x 1 + 552
We consider the new divisor 1622 and the new remainder 552,and apply the division lemma to get
1622 = 552 x 2 + 518
We consider the new divisor 552 and the new remainder 518,and apply the division lemma to get
552 = 518 x 1 + 34
We consider the new divisor 518 and the new remainder 34,and apply the division lemma to get
518 = 34 x 15 + 8
We consider the new divisor 34 and the new remainder 8,and apply the division lemma to get
34 = 8 x 4 + 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 9766 and 5970 is 2
Notice that 2 = HCF(8,2) = HCF(34,8) = HCF(518,34) = HCF(552,518) = HCF(1622,552) = HCF(2174,1622) = HCF(3796,2174) = HCF(5970,3796) = HCF(9766,5970) .
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Frequently Asked Questions on HCF of 9766, 5970 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 9766, 5970?
Answer: HCF of 9766, 5970 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9766, 5970 using Euclid's Algorithm?
Answer: For arbitrary numbers 9766, 5970 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.