Highest Common Factor of 372, 643 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 372, 643 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 372, 643 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 372, 643 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 372, 643 is 1.
HCF(372, 643) = 1
HCF of 372, 643 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 372, 643 is 1.
Highest Common Factor of 372,643 is 1
Step 1: Since 643 > 372, we apply the division lemma to 643 and 372, to get
643 = 372 x 1 + 271
Step 2: Since the reminder 372 ≠ 0, we apply division lemma to 271 and 372, to get
372 = 271 x 1 + 101
Step 3: We consider the new divisor 271 and the new remainder 101, and apply the division lemma to get
271 = 101 x 2 + 69
We consider the new divisor 101 and the new remainder 69,and apply the division lemma to get
101 = 69 x 1 + 32
We consider the new divisor 69 and the new remainder 32,and apply the division lemma to get
69 = 32 x 2 + 5
We consider the new divisor 32 and the new remainder 5,and apply the division lemma to get
32 = 5 x 6 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 372 and 643 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(32,5) = HCF(69,32) = HCF(101,69) = HCF(271,101) = HCF(372,271) = HCF(643,372) .
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Frequently Asked Questions on HCF of 372, 643 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 372, 643?
Answer: HCF of 372, 643 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 372, 643 using Euclid's Algorithm?
Answer: For arbitrary numbers 372, 643 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.