Highest Common Factor of 966, 710 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 966, 710 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 966, 710 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 966, 710 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 966, 710 is 2.
HCF(966, 710) = 2
HCF of 966, 710 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 966, 710 is 2.
Highest Common Factor of 966,710 is 2
Step 1: Since 966 > 710, we apply the division lemma to 966 and 710, to get
966 = 710 x 1 + 256
Step 2: Since the reminder 710 ≠ 0, we apply division lemma to 256 and 710, to get
710 = 256 x 2 + 198
Step 3: We consider the new divisor 256 and the new remainder 198, and apply the division lemma to get
256 = 198 x 1 + 58
We consider the new divisor 198 and the new remainder 58,and apply the division lemma to get
198 = 58 x 3 + 24
We consider the new divisor 58 and the new remainder 24,and apply the division lemma to get
58 = 24 x 2 + 10
We consider the new divisor 24 and the new remainder 10,and apply the division lemma to get
24 = 10 x 2 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 966 and 710 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(24,10) = HCF(58,24) = HCF(198,58) = HCF(256,198) = HCF(710,256) = HCF(966,710) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 966, 710 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 966, 710?
Answer: HCF of 966, 710 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 966, 710 using Euclid's Algorithm?
Answer: For arbitrary numbers 966, 710 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.