Highest Common Factor of 642, 408, 687 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 642, 408, 687 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 642, 408, 687 is 3 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 642, 408, 687 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 642, 408, 687 is 3.
HCF(642, 408, 687) = 3
HCF of 642, 408, 687 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 642, 408, 687 is 3.
Highest Common Factor of 642,408,687 is 3
Step 1: Since 642 > 408, we apply the division lemma to 642 and 408, to get
642 = 408 x 1 + 234
Step 2: Since the reminder 408 ≠ 0, we apply division lemma to 234 and 408, to get
408 = 234 x 1 + 174
Step 3: We consider the new divisor 234 and the new remainder 174, and apply the division lemma to get
234 = 174 x 1 + 60
We consider the new divisor 174 and the new remainder 60,and apply the division lemma to get
174 = 60 x 2 + 54
We consider the new divisor 60 and the new remainder 54,and apply the division lemma to get
60 = 54 x 1 + 6
We consider the new divisor 54 and the new remainder 6,and apply the division lemma to get
54 = 6 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 642 and 408 is 6
Notice that 6 = HCF(54,6) = HCF(60,54) = HCF(174,60) = HCF(234,174) = HCF(408,234) = HCF(642,408) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 687 > 6, we apply the division lemma to 687 and 6, to get
687 = 6 x 114 + 3
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 3 and 6, to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 6 and 687 is 3
Notice that 3 = HCF(6,3) = HCF(687,6) .
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Frequently Asked Questions on HCF of 642, 408, 687 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 642, 408, 687?
Answer: HCF of 642, 408, 687 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 642, 408, 687 using Euclid's Algorithm?
Answer: For arbitrary numbers 642, 408, 687 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.