Highest Common Factor of 665, 540, 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 665, 540, 431 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 665, 540, 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 665, 540, 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 665, 540, 431 is 1.
HCF(665, 540, 431) = 1
HCF of 665, 540, 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 665, 540, 431 is 1.
Highest Common Factor of 665,540,431 is 1
Step 1: Since 665 > 540, we apply the division lemma to 665 and 540, to get
665 = 540 x 1 + 125
Step 2: Since the reminder 540 ≠ 0, we apply division lemma to 125 and 540, to get
540 = 125 x 4 + 40
Step 3: We consider the new divisor 125 and the new remainder 40, and apply the division lemma to get
125 = 40 x 3 + 5
We consider the new divisor 40 and the new remainder 5, and apply the division lemma to get
40 = 5 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 665 and 540 is 5
Notice that 5 = HCF(40,5) = HCF(125,40) = HCF(540,125) = HCF(665,540) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 431 > 5, we apply the division lemma to 431 and 5, to get
431 = 5 x 86 + 1
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 1 and 5, to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 431 is 1
Notice that 1 = HCF(5,1) = HCF(431,5) .
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Frequently Asked Questions on HCF of 665, 540, 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 665, 540, 431?
Answer: HCF of 665, 540, 431 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 665, 540, 431 using Euclid's Algorithm?
Answer: For arbitrary numbers 665, 540, 431 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
