Highest Common Factor of 413, 517, 60 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, 517, 60 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 413, 517, 60 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, 517, 60 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, 517, 60 is 1.
HCF(413, 517, 60) = 1
HCF of 413, 517, 60 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, 517, 60 is 1.
Highest Common Factor of 413,517,60 is 1
Step 1: Since 517 > 413, we apply the division lemma to 517 and 413, to get
517 = 413 x 1 + 104
Step 2: Since the reminder 413 ≠ 0, we apply division lemma to 104 and 413, to get
413 = 104 x 3 + 101
Step 3: We consider the new divisor 104 and the new remainder 101, and apply the division lemma to get
104 = 101 x 1 + 3
We consider the new divisor 101 and the new remainder 3,and apply the division lemma to get
101 = 3 x 33 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 413 and 517 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(101,3) = HCF(104,101) = HCF(413,104) = HCF(517,413) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 60 > 1, we apply the division lemma to 60 and 1, to get
60 = 1 x 60 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 60 is 1
Notice that 1 = HCF(60,1) .
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Frequently Asked Questions on HCF of 413, 517, 60 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, 517, 60?
Answer: HCF of 413, 517, 60 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 413, 517, 60 using Euclid's Algorithm?
Answer: For arbitrary numbers 413, 517, 60 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.