Highest Common Factor of 966, 310 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, 310 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 966, 310 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, 310 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, 310 is 2.
HCF(966, 310) = 2
HCF of 966, 310 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, 310 is 2.
Highest Common Factor of 966,310 is 2
Step 1: Since 966 > 310, we apply the division lemma to 966 and 310, to get
966 = 310 x 3 + 36
Step 2: Since the reminder 310 ≠ 0, we apply division lemma to 36 and 310, to get
310 = 36 x 8 + 22
Step 3: We consider the new divisor 36 and the new remainder 22, and apply the division lemma to get
36 = 22 x 1 + 14
We consider the new divisor 22 and the new remainder 14,and apply the division lemma to get
22 = 14 x 1 + 8
We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get
14 = 8 x 1 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 966 and 310 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(22,14) = HCF(36,22) = HCF(310,36) = HCF(966,310) .
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Frequently Asked Questions on HCF of 966, 310 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, 310?
Answer: HCF of 966, 310 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 966, 310 using Euclid's Algorithm?
Answer: For arbitrary numbers 966, 310 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.