Highest Common Factor of 9722, 1020 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 9722, 1020 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 9722, 1020 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 9722, 1020 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 9722, 1020 is 2.
HCF(9722, 1020) = 2
HCF of 9722, 1020 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9722, 1020 is 2.
Highest Common Factor of 9722,1020 is 2
Step 1: Since 9722 > 1020, we apply the division lemma to 9722 and 1020, to get
9722 = 1020 x 9 + 542
Step 2: Since the reminder 1020 ≠ 0, we apply division lemma to 542 and 1020, to get
1020 = 542 x 1 + 478
Step 3: We consider the new divisor 542 and the new remainder 478, and apply the division lemma to get
542 = 478 x 1 + 64
We consider the new divisor 478 and the new remainder 64,and apply the division lemma to get
478 = 64 x 7 + 30
We consider the new divisor 64 and the new remainder 30,and apply the division lemma to get
64 = 30 x 2 + 4
We consider the new divisor 30 and the new remainder 4,and apply the division lemma to get
30 = 4 x 7 + 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 9722 and 1020 is 2
Notice that 2 = HCF(4,2) = HCF(30,4) = HCF(64,30) = HCF(478,64) = HCF(542,478) = HCF(1020,542) = HCF(9722,1020) .
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Frequently Asked Questions on HCF of 9722, 1020 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 9722, 1020?
Answer: HCF of 9722, 1020 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9722, 1020 using Euclid's Algorithm?
Answer: For arbitrary numbers 9722, 1020 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.