Highest Common Factor of 657, 912 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 657, 912 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 657, 912 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 657, 912 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 657, 912 is 3.
HCF(657, 912) = 3
HCF of 657, 912 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 657, 912 is 3.
Highest Common Factor of 657,912 is 3
Step 1: Since 912 > 657, we apply the division lemma to 912 and 657, to get
912 = 657 x 1 + 255
Step 2: Since the reminder 657 ≠ 0, we apply division lemma to 255 and 657, to get
657 = 255 x 2 + 147
Step 3: We consider the new divisor 255 and the new remainder 147, and apply the division lemma to get
255 = 147 x 1 + 108
We consider the new divisor 147 and the new remainder 108,and apply the division lemma to get
147 = 108 x 1 + 39
We consider the new divisor 108 and the new remainder 39,and apply the division lemma to get
108 = 39 x 2 + 30
We consider the new divisor 39 and the new remainder 30,and apply the division lemma to get
39 = 30 x 1 + 9
We consider the new divisor 30 and the new remainder 9,and apply the division lemma to get
30 = 9 x 3 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 657 and 912 is 3
Notice that 3 = HCF(9,3) = HCF(30,9) = HCF(39,30) = HCF(108,39) = HCF(147,108) = HCF(255,147) = HCF(657,255) = HCF(912,657) .
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Frequently Asked Questions on HCF of 657, 912 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 657, 912?
Answer: HCF of 657, 912 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 657, 912 using Euclid's Algorithm?
Answer: For arbitrary numbers 657, 912 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.