Highest Common Factor of 4374, 742 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 4374, 742 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 4374, 742 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 4374, 742 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 4374, 742 is 2.
HCF(4374, 742) = 2
HCF of 4374, 742 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 4374, 742 is 2.
Highest Common Factor of 4374,742 is 2
Step 1: Since 4374 > 742, we apply the division lemma to 4374 and 742, to get
4374 = 742 x 5 + 664
Step 2: Since the reminder 742 ≠ 0, we apply division lemma to 664 and 742, to get
742 = 664 x 1 + 78
Step 3: We consider the new divisor 664 and the new remainder 78, and apply the division lemma to get
664 = 78 x 8 + 40
We consider the new divisor 78 and the new remainder 40,and apply the division lemma to get
78 = 40 x 1 + 38
We consider the new divisor 40 and the new remainder 38,and apply the division lemma to get
40 = 38 x 1 + 2
We consider the new divisor 38 and the new remainder 2,and apply the division lemma to get
38 = 2 x 19 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4374 and 742 is 2
Notice that 2 = HCF(38,2) = HCF(40,38) = HCF(78,40) = HCF(664,78) = HCF(742,664) = HCF(4374,742) .
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Frequently Asked Questions on HCF of 4374, 742 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 4374, 742?
Answer: HCF of 4374, 742 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 4374, 742 using Euclid's Algorithm?
Answer: For arbitrary numbers 4374, 742 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.