Highest Common Factor of 672, 584, 642 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 672, 584, 642 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 672, 584, 642 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 672, 584, 642 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 672, 584, 642 is 2.
HCF(672, 584, 642) = 2
HCF of 672, 584, 642 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 672, 584, 642 is 2.
Highest Common Factor of 672,584,642 is 2
Step 1: Since 672 > 584, we apply the division lemma to 672 and 584, to get
672 = 584 x 1 + 88
Step 2: Since the reminder 584 ≠ 0, we apply division lemma to 88 and 584, to get
584 = 88 x 6 + 56
Step 3: We consider the new divisor 88 and the new remainder 56, and apply the division lemma to get
88 = 56 x 1 + 32
We consider the new divisor 56 and the new remainder 32,and apply the division lemma to get
56 = 32 x 1 + 24
We consider the new divisor 32 and the new remainder 24,and apply the division lemma to get
32 = 24 x 1 + 8
We consider the new divisor 24 and the new remainder 8,and apply the division lemma to get
24 = 8 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 672 and 584 is 8
Notice that 8 = HCF(24,8) = HCF(32,24) = HCF(56,32) = HCF(88,56) = HCF(584,88) = HCF(672,584) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 642 > 8, we apply the division lemma to 642 and 8, to get
642 = 8 x 80 + 2
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 2 and 8, to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8 and 642 is 2
Notice that 2 = HCF(8,2) = HCF(642,8) .
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Frequently Asked Questions on HCF of 672, 584, 642 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 672, 584, 642?
Answer: HCF of 672, 584, 642 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 672, 584, 642 using Euclid's Algorithm?
Answer: For arbitrary numbers 672, 584, 642 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.