Highest Common Factor of 457, 724 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 457, 724 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 457, 724 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 457, 724 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 457, 724 is 1.
HCF(457, 724) = 1
HCF of 457, 724 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 457, 724 is 1.
Highest Common Factor of 457,724 is 1
Step 1: Since 724 > 457, we apply the division lemma to 724 and 457, to get
724 = 457 x 1 + 267
Step 2: Since the reminder 457 ≠ 0, we apply division lemma to 267 and 457, to get
457 = 267 x 1 + 190
Step 3: We consider the new divisor 267 and the new remainder 190, and apply the division lemma to get
267 = 190 x 1 + 77
We consider the new divisor 190 and the new remainder 77,and apply the division lemma to get
190 = 77 x 2 + 36
We consider the new divisor 77 and the new remainder 36,and apply the division lemma to get
77 = 36 x 2 + 5
We consider the new divisor 36 and the new remainder 5,and apply the division lemma to get
36 = 5 x 7 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 457 and 724 is 1
Notice that 1 = HCF(5,1) = HCF(36,5) = HCF(77,36) = HCF(190,77) = HCF(267,190) = HCF(457,267) = HCF(724,457) .
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Frequently Asked Questions on HCF of 457, 724 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 457, 724?
Answer: HCF of 457, 724 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 457, 724 using Euclid's Algorithm?
Answer: For arbitrary numbers 457, 724 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.