Highest Common Factor of 657, 900 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, 900 i.e. 9 the largest integer that leaves a remainder zero for all numbers.
HCF of 657, 900 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 657, 900 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, 900 is 9.
HCF(657, 900) = 9
HCF of 657, 900 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, 900 is 9.
Highest Common Factor of 657,900 is 9
Step 1: Since 900 > 657, we apply the division lemma to 900 and 657, to get
900 = 657 x 1 + 243
Step 2: Since the reminder 657 ≠ 0, we apply division lemma to 243 and 657, to get
657 = 243 x 2 + 171
Step 3: We consider the new divisor 243 and the new remainder 171, and apply the division lemma to get
243 = 171 x 1 + 72
We consider the new divisor 171 and the new remainder 72,and apply the division lemma to get
171 = 72 x 2 + 27
We consider the new divisor 72 and the new remainder 27,and apply the division lemma to get
72 = 27 x 2 + 18
We consider the new divisor 27 and the new remainder 18,and apply the division lemma to get
27 = 18 x 1 + 9
We consider the new divisor 18 and the new remainder 9,and apply the division lemma to get
18 = 9 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 657 and 900 is 9
Notice that 9 = HCF(18,9) = HCF(27,18) = HCF(72,27) = HCF(171,72) = HCF(243,171) = HCF(657,243) = HCF(900,657) .
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Frequently Asked Questions on HCF of 657, 900 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, 900?
Answer: HCF of 657, 900 is 9 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 657, 900 using Euclid's Algorithm?
Answer: For arbitrary numbers 657, 900 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
