Highest Common Factor of 612, 108, 657 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 612, 108, 657 i.e. 9 the largest integer that leaves a remainder zero for all numbers.
HCF of 612, 108, 657 is 9 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 612, 108, 657 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 612, 108, 657 is 9.
HCF(612, 108, 657) = 9
HCF of 612, 108, 657 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 612, 108, 657 is 9.
Highest Common Factor of 612,108,657 is 9
Step 1: Since 612 > 108, we apply the division lemma to 612 and 108, to get
612 = 108 x 5 + 72
Step 2: Since the reminder 108 ≠ 0, we apply division lemma to 72 and 108, to get
108 = 72 x 1 + 36
Step 3: We consider the new divisor 72 and the new remainder 36, and apply the division lemma to get
72 = 36 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 36, the HCF of 612 and 108 is 36
Notice that 36 = HCF(72,36) = HCF(108,72) = HCF(612,108) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 657 > 36, we apply the division lemma to 657 and 36, to get
657 = 36 x 18 + 9
Step 2: Since the reminder 36 ≠ 0, we apply division lemma to 9 and 36, to get
36 = 9 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 36 and 657 is 9
Notice that 9 = HCF(36,9) = HCF(657,36) .
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Frequently Asked Questions on HCF of 612, 108, 657 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 612, 108, 657?
Answer: HCF of 612, 108, 657 is 9 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 612, 108, 657 using Euclid's Algorithm?
Answer: For arbitrary numbers 612, 108, 657 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.