Highest Common Factor of 517, 1652 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 517, 1652 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 517, 1652 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 517, 1652 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 517, 1652 is 1.
HCF(517, 1652) = 1
HCF of 517, 1652 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 517, 1652 is 1.
Highest Common Factor of 517,1652 is 1
Step 1: Since 1652 > 517, we apply the division lemma to 1652 and 517, to get
1652 = 517 x 3 + 101
Step 2: Since the reminder 517 ≠ 0, we apply division lemma to 101 and 517, to get
517 = 101 x 5 + 12
Step 3: We consider the new divisor 101 and the new remainder 12, and apply the division lemma to get
101 = 12 x 8 + 5
We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get
12 = 5 x 2 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 517 and 1652 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(101,12) = HCF(517,101) = HCF(1652,517) .
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Frequently Asked Questions on HCF of 517, 1652 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 517, 1652?
Answer: HCF of 517, 1652 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 517, 1652 using Euclid's Algorithm?
Answer: For arbitrary numbers 517, 1652 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.