Highest Common Factor of 1422, 3664 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 1422, 3664 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 1422, 3664 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 1422, 3664 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 1422, 3664 is 2.
HCF(1422, 3664) = 2
HCF of 1422, 3664 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1422, 3664 is 2.
Highest Common Factor of 1422,3664 is 2
Step 1: Since 3664 > 1422, we apply the division lemma to 3664 and 1422, to get
3664 = 1422 x 2 + 820
Step 2: Since the reminder 1422 ≠ 0, we apply division lemma to 820 and 1422, to get
1422 = 820 x 1 + 602
Step 3: We consider the new divisor 820 and the new remainder 602, and apply the division lemma to get
820 = 602 x 1 + 218
We consider the new divisor 602 and the new remainder 218,and apply the division lemma to get
602 = 218 x 2 + 166
We consider the new divisor 218 and the new remainder 166,and apply the division lemma to get
218 = 166 x 1 + 52
We consider the new divisor 166 and the new remainder 52,and apply the division lemma to get
166 = 52 x 3 + 10
We consider the new divisor 52 and the new remainder 10,and apply the division lemma to get
52 = 10 x 5 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 1422 and 3664 is 2
Notice that 2 = HCF(10,2) = HCF(52,10) = HCF(166,52) = HCF(218,166) = HCF(602,218) = HCF(820,602) = HCF(1422,820) = HCF(3664,1422) .
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Frequently Asked Questions on HCF of 1422, 3664 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 1422, 3664?
Answer: HCF of 1422, 3664 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1422, 3664 using Euclid's Algorithm?
Answer: For arbitrary numbers 1422, 3664 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.