Highest Common Factor of 413, 767, 540 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 413, 767, 540 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 413, 767, 540 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 413, 767, 540 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 413, 767, 540 is 1.
HCF(413, 767, 540) = 1
HCF of 413, 767, 540 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 413, 767, 540 is 1.
Highest Common Factor of 413,767,540 is 1
Step 1: Since 767 > 413, we apply the division lemma to 767 and 413, to get
767 = 413 x 1 + 354
Step 2: Since the reminder 413 ≠ 0, we apply division lemma to 354 and 413, to get
413 = 354 x 1 + 59
Step 3: We consider the new divisor 354 and the new remainder 59, and apply the division lemma to get
354 = 59 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 59, the HCF of 413 and 767 is 59
Notice that 59 = HCF(354,59) = HCF(413,354) = HCF(767,413) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 540 > 59, we apply the division lemma to 540 and 59, to get
540 = 59 x 9 + 9
Step 2: Since the reminder 59 ≠ 0, we apply division lemma to 9 and 59, to get
59 = 9 x 6 + 5
Step 3: We consider the new divisor 9 and the new remainder 5, and apply the division lemma to get
9 = 5 x 1 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 59 and 540 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(59,9) = HCF(540,59) .
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Frequently Asked Questions on HCF of 413, 767, 540 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 413, 767, 540?
Answer: HCF of 413, 767, 540 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 413, 767, 540 using Euclid's Algorithm?
Answer: For arbitrary numbers 413, 767, 540 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
