Highest Common Factor of 752, 674 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 752, 674 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 752, 674 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 752, 674 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 752, 674 is 2.
HCF(752, 674) = 2
HCF of 752, 674 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 752, 674 is 2.
Highest Common Factor of 752,674 is 2
Step 1: Since 752 > 674, we apply the division lemma to 752 and 674, to get
752 = 674 x 1 + 78
Step 2: Since the reminder 674 ≠ 0, we apply division lemma to 78 and 674, to get
674 = 78 x 8 + 50
Step 3: We consider the new divisor 78 and the new remainder 50, and apply the division lemma to get
78 = 50 x 1 + 28
We consider the new divisor 50 and the new remainder 28,and apply the division lemma to get
50 = 28 x 1 + 22
We consider the new divisor 28 and the new remainder 22,and apply the division lemma to get
28 = 22 x 1 + 6
We consider the new divisor 22 and the new remainder 6,and apply the division lemma to get
22 = 6 x 3 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 752 and 674 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(22,6) = HCF(28,22) = HCF(50,28) = HCF(78,50) = HCF(674,78) = HCF(752,674) .
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Frequently Asked Questions on HCF of 752, 674 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 752, 674?
Answer: HCF of 752, 674 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 752, 674 using Euclid's Algorithm?
Answer: For arbitrary numbers 752, 674 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.