Highest Common Factor of 966, 39396 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, 39396 i.e. 42 the largest integer that leaves a remainder zero for all numbers.
HCF of 966, 39396 is 42 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, 39396 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, 39396 is 42.
HCF(966, 39396) = 42
HCF of 966, 39396 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, 39396 is 42.
Highest Common Factor of 966,39396 is 42
Step 1: Since 39396 > 966, we apply the division lemma to 39396 and 966, to get
39396 = 966 x 40 + 756
Step 2: Since the reminder 966 ≠ 0, we apply division lemma to 756 and 966, to get
966 = 756 x 1 + 210
Step 3: We consider the new divisor 756 and the new remainder 210, and apply the division lemma to get
756 = 210 x 3 + 126
We consider the new divisor 210 and the new remainder 126,and apply the division lemma to get
210 = 126 x 1 + 84
We consider the new divisor 126 and the new remainder 84,and apply the division lemma to get
126 = 84 x 1 + 42
We consider the new divisor 84 and the new remainder 42,and apply the division lemma to get
84 = 42 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 42, the HCF of 966 and 39396 is 42
Notice that 42 = HCF(84,42) = HCF(126,84) = HCF(210,126) = HCF(756,210) = HCF(966,756) = HCF(39396,966) .
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Frequently Asked Questions on HCF of 966, 39396 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, 39396?
Answer: HCF of 966, 39396 is 42 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 966, 39396 using Euclid's Algorithm?
Answer: For arbitrary numbers 966, 39396 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
