Highest Common Factor of 674, 612 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 674, 612 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 674, 612 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 674, 612 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 674, 612 is 2.
HCF(674, 612) = 2
HCF of 674, 612 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 674, 612 is 2.
Highest Common Factor of 674,612 is 2
Step 1: Since 674 > 612, we apply the division lemma to 674 and 612, to get
674 = 612 x 1 + 62
Step 2: Since the reminder 612 ≠ 0, we apply division lemma to 62 and 612, to get
612 = 62 x 9 + 54
Step 3: We consider the new divisor 62 and the new remainder 54, and apply the division lemma to get
62 = 54 x 1 + 8
We consider the new divisor 54 and the new remainder 8,and apply the division lemma to get
54 = 8 x 6 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 674 and 612 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(54,8) = HCF(62,54) = HCF(612,62) = HCF(674,612) .
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Frequently Asked Questions on HCF of 674, 612 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 674, 612?
Answer: HCF of 674, 612 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 674, 612 using Euclid's Algorithm?
Answer: For arbitrary numbers 674, 612 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.