Highest Common Factor of 424, 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 424, 724 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 424, 724 is 4 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 424, 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 424, 724 is 4.
HCF(424, 724) = 4
HCF of 424, 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 424, 724 is 4.
Highest Common Factor of 424,724 is 4
Step 1: Since 724 > 424, we apply the division lemma to 724 and 424, to get
724 = 424 x 1 + 300
Step 2: Since the reminder 424 ≠ 0, we apply division lemma to 300 and 424, to get
424 = 300 x 1 + 124
Step 3: We consider the new divisor 300 and the new remainder 124, and apply the division lemma to get
300 = 124 x 2 + 52
We consider the new divisor 124 and the new remainder 52,and apply the division lemma to get
124 = 52 x 2 + 20
We consider the new divisor 52 and the new remainder 20,and apply the division lemma to get
52 = 20 x 2 + 12
We consider the new divisor 20 and the new remainder 12,and apply the division lemma to get
20 = 12 x 1 + 8
We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get
12 = 8 x 1 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 424 and 724 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(20,12) = HCF(52,20) = HCF(124,52) = HCF(300,124) = HCF(424,300) = HCF(724,424) .
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Frequently Asked Questions on HCF of 424, 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 424, 724?
Answer: HCF of 424, 724 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 424, 724 using Euclid's Algorithm?
Answer: For arbitrary numbers 424, 724 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.