Highest Common Factor of 8122, 2421 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 8122, 2421 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 8122, 2421 is 1 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 8122, 2421 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 8122, 2421 is 1.
HCF(8122, 2421) = 1
HCF of 8122, 2421 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8122, 2421 is 1.
Highest Common Factor of 8122,2421 is 1
Step 1: Since 8122 > 2421, we apply the division lemma to 8122 and 2421, to get
8122 = 2421 x 3 + 859
Step 2: Since the reminder 2421 ≠ 0, we apply division lemma to 859 and 2421, to get
2421 = 859 x 2 + 703
Step 3: We consider the new divisor 859 and the new remainder 703, and apply the division lemma to get
859 = 703 x 1 + 156
We consider the new divisor 703 and the new remainder 156,and apply the division lemma to get
703 = 156 x 4 + 79
We consider the new divisor 156 and the new remainder 79,and apply the division lemma to get
156 = 79 x 1 + 77
We consider the new divisor 79 and the new remainder 77,and apply the division lemma to get
79 = 77 x 1 + 2
We consider the new divisor 77 and the new remainder 2,and apply the division lemma to get
77 = 2 x 38 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8122 and 2421 is 1
Notice that 1 = HCF(2,1) = HCF(77,2) = HCF(79,77) = HCF(156,79) = HCF(703,156) = HCF(859,703) = HCF(2421,859) = HCF(8122,2421) .
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Frequently Asked Questions on HCF of 8122, 2421 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 8122, 2421?
Answer: HCF of 8122, 2421 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8122, 2421 using Euclid's Algorithm?
Answer: For arbitrary numbers 8122, 2421 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.