Highest Common Factor of 888, 657 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 888, 657 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 888, 657 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 888, 657 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 888, 657 is 3.
HCF(888, 657) = 3
HCF of 888, 657 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 888, 657 is 3.
Highest Common Factor of 888,657 is 3
Step 1: Since 888 > 657, we apply the division lemma to 888 and 657, to get
888 = 657 x 1 + 231
Step 2: Since the reminder 657 ≠ 0, we apply division lemma to 231 and 657, to get
657 = 231 x 2 + 195
Step 3: We consider the new divisor 231 and the new remainder 195, and apply the division lemma to get
231 = 195 x 1 + 36
We consider the new divisor 195 and the new remainder 36,and apply the division lemma to get
195 = 36 x 5 + 15
We consider the new divisor 36 and the new remainder 15,and apply the division lemma to get
36 = 15 x 2 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 888 and 657 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(36,15) = HCF(195,36) = HCF(231,195) = HCF(657,231) = HCF(888,657) .
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Frequently Asked Questions on HCF of 888, 657 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 888, 657?
Answer: HCF of 888, 657 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 888, 657 using Euclid's Algorithm?
Answer: For arbitrary numbers 888, 657 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.