Highest Common Factor of 657, 7420 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, 7420 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 657, 7420 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, 7420 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, 7420 is 1.
HCF(657, 7420) = 1
HCF of 657, 7420 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, 7420 is 1.
Highest Common Factor of 657,7420 is 1
Step 1: Since 7420 > 657, we apply the division lemma to 7420 and 657, to get
7420 = 657 x 11 + 193
Step 2: Since the reminder 657 ≠ 0, we apply division lemma to 193 and 657, to get
657 = 193 x 3 + 78
Step 3: We consider the new divisor 193 and the new remainder 78, and apply the division lemma to get
193 = 78 x 2 + 37
We consider the new divisor 78 and the new remainder 37,and apply the division lemma to get
78 = 37 x 2 + 4
We consider the new divisor 37 and the new remainder 4,and apply the division lemma to get
37 = 4 x 9 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 657 and 7420 is 1
Notice that 1 = HCF(4,1) = HCF(37,4) = HCF(78,37) = HCF(193,78) = HCF(657,193) = HCF(7420,657) .
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Frequently Asked Questions on HCF of 657, 7420 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, 7420?
Answer: HCF of 657, 7420 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 657, 7420 using Euclid's Algorithm?
Answer: For arbitrary numbers 657, 7420 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.