Highest Common Factor of 660, 431 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 660, 431 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 660, 431 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 660, 431 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 660, 431 is 1.
HCF(660, 431) = 1
HCF of 660, 431 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 660, 431 is 1.
Highest Common Factor of 660,431 is 1
Step 1: Since 660 > 431, we apply the division lemma to 660 and 431, to get
660 = 431 x 1 + 229
Step 2: Since the reminder 431 ≠ 0, we apply division lemma to 229 and 431, to get
431 = 229 x 1 + 202
Step 3: We consider the new divisor 229 and the new remainder 202, and apply the division lemma to get
229 = 202 x 1 + 27
We consider the new divisor 202 and the new remainder 27,and apply the division lemma to get
202 = 27 x 7 + 13
We consider the new divisor 27 and the new remainder 13,and apply the division lemma to get
27 = 13 x 2 + 1
We consider the new divisor 13 and the new remainder 1,and apply the division lemma to get
13 = 1 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 660 and 431 is 1
Notice that 1 = HCF(13,1) = HCF(27,13) = HCF(202,27) = HCF(229,202) = HCF(431,229) = HCF(660,431) .
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Frequently Asked Questions on HCF of 660, 431 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 660, 431?
Answer: HCF of 660, 431 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 660, 431 using Euclid's Algorithm?
Answer: For arbitrary numbers 660, 431 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.