Highest Common Factor of 674, 464, 584 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, 464, 584 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 674, 464, 584 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, 464, 584 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, 464, 584 is 2.
HCF(674, 464, 584) = 2
HCF of 674, 464, 584 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, 464, 584 is 2.
Highest Common Factor of 674,464,584 is 2
Step 1: Since 674 > 464, we apply the division lemma to 674 and 464, to get
674 = 464 x 1 + 210
Step 2: Since the reminder 464 ≠ 0, we apply division lemma to 210 and 464, to get
464 = 210 x 2 + 44
Step 3: We consider the new divisor 210 and the new remainder 44, and apply the division lemma to get
210 = 44 x 4 + 34
We consider the new divisor 44 and the new remainder 34,and apply the division lemma to get
44 = 34 x 1 + 10
We consider the new divisor 34 and the new remainder 10,and apply the division lemma to get
34 = 10 x 3 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 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 464 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(34,10) = HCF(44,34) = HCF(210,44) = HCF(464,210) = HCF(674,464) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 584 > 2, we apply the division lemma to 584 and 2, to get
584 = 2 x 292 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 584 is 2
Notice that 2 = HCF(584,2) .
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Frequently Asked Questions on HCF of 674, 464, 584 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, 464, 584?
Answer: HCF of 674, 464, 584 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 674, 464, 584 using Euclid's Algorithm?
Answer: For arbitrary numbers 674, 464, 584 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.