Highest Common Factor of 657, 412 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, 412 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 657, 412 is 1 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, 412 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, 412 is 1.
HCF(657, 412) = 1
HCF of 657, 412 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, 412 is 1.
Highest Common Factor of 657,412 is 1
Step 1: Since 657 > 412, we apply the division lemma to 657 and 412, to get
657 = 412 x 1 + 245
Step 2: Since the reminder 412 ≠ 0, we apply division lemma to 245 and 412, to get
412 = 245 x 1 + 167
Step 3: We consider the new divisor 245 and the new remainder 167, and apply the division lemma to get
245 = 167 x 1 + 78
We consider the new divisor 167 and the new remainder 78,and apply the division lemma to get
167 = 78 x 2 + 11
We consider the new divisor 78 and the new remainder 11,and apply the division lemma to get
78 = 11 x 7 + 1
We consider the new divisor 11 and the new remainder 1,and apply the division lemma to get
11 = 1 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 657 and 412 is 1
Notice that 1 = HCF(11,1) = HCF(78,11) = HCF(167,78) = HCF(245,167) = HCF(412,245) = HCF(657,412) .
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Frequently Asked Questions on HCF of 657, 412 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, 412?
Answer: HCF of 657, 412 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 657, 412 using Euclid's Algorithm?
Answer: For arbitrary numbers 657, 412 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.