Highest Common Factor of 6657, 5964 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 6657, 5964 i.e. 21 the largest integer that leaves a remainder zero for all numbers.
HCF of 6657, 5964 is 21 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 6657, 5964 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 6657, 5964 is 21.
HCF(6657, 5964) = 21
HCF of 6657, 5964 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6657, 5964 is 21.
Highest Common Factor of 6657,5964 is 21
Step 1: Since 6657 > 5964, we apply the division lemma to 6657 and 5964, to get
6657 = 5964 x 1 + 693
Step 2: Since the reminder 5964 ≠ 0, we apply division lemma to 693 and 5964, to get
5964 = 693 x 8 + 420
Step 3: We consider the new divisor 693 and the new remainder 420, and apply the division lemma to get
693 = 420 x 1 + 273
We consider the new divisor 420 and the new remainder 273,and apply the division lemma to get
420 = 273 x 1 + 147
We consider the new divisor 273 and the new remainder 147,and apply the division lemma to get
273 = 147 x 1 + 126
We consider the new divisor 147 and the new remainder 126,and apply the division lemma to get
147 = 126 x 1 + 21
We consider the new divisor 126 and the new remainder 21,and apply the division lemma to get
126 = 21 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 21, the HCF of 6657 and 5964 is 21
Notice that 21 = HCF(126,21) = HCF(147,126) = HCF(273,147) = HCF(420,273) = HCF(693,420) = HCF(5964,693) = HCF(6657,5964) .
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Frequently Asked Questions on HCF of 6657, 5964 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 6657, 5964?
Answer: HCF of 6657, 5964 is 21 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6657, 5964 using Euclid's Algorithm?
Answer: For arbitrary numbers 6657, 5964 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.