Highest Common Factor of 674, 60944 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, 60944 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 674, 60944 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, 60944 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, 60944 is 2.
HCF(674, 60944) = 2
HCF of 674, 60944 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, 60944 is 2.
Highest Common Factor of 674,60944 is 2
Step 1: Since 60944 > 674, we apply the division lemma to 60944 and 674, to get
60944 = 674 x 90 + 284
Step 2: Since the reminder 674 ≠ 0, we apply division lemma to 284 and 674, to get
674 = 284 x 2 + 106
Step 3: We consider the new divisor 284 and the new remainder 106, and apply the division lemma to get
284 = 106 x 2 + 72
We consider the new divisor 106 and the new remainder 72,and apply the division lemma to get
106 = 72 x 1 + 34
We consider the new divisor 72 and the new remainder 34,and apply the division lemma to get
72 = 34 x 2 + 4
We consider the new divisor 34 and the new remainder 4,and apply the division lemma to get
34 = 4 x 8 + 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 674 and 60944 is 2
Notice that 2 = HCF(4,2) = HCF(34,4) = HCF(72,34) = HCF(106,72) = HCF(284,106) = HCF(674,284) = HCF(60944,674) .
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Frequently Asked Questions on HCF of 674, 60944 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, 60944?
Answer: HCF of 674, 60944 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 674, 60944 using Euclid's Algorithm?
Answer: For arbitrary numbers 674, 60944 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.