Highest Common Factor of 963, 1971 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 963, 1971 i.e. 9 the largest integer that leaves a remainder zero for all numbers.
HCF of 963, 1971 is 9 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 963, 1971 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 963, 1971 is 9.
HCF(963, 1971) = 9
HCF of 963, 1971 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 963, 1971 is 9.
Highest Common Factor of 963,1971 is 9
Step 1: Since 1971 > 963, we apply the division lemma to 1971 and 963, to get
1971 = 963 x 2 + 45
Step 2: Since the reminder 963 ≠ 0, we apply division lemma to 45 and 963, to get
963 = 45 x 21 + 18
Step 3: We consider the new divisor 45 and the new remainder 18, and apply the division lemma to get
45 = 18 x 2 + 9
We consider the new divisor 18 and the new remainder 9, and apply the division lemma to get
18 = 9 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 963 and 1971 is 9
Notice that 9 = HCF(18,9) = HCF(45,18) = HCF(963,45) = HCF(1971,963) .
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Frequently Asked Questions on HCF of 963, 1971 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 963, 1971?
Answer: HCF of 963, 1971 is 9 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 963, 1971 using Euclid's Algorithm?
Answer: For arbitrary numbers 963, 1971 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.