Highest Common Factor of 413, 652 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, 652 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 413, 652 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, 652 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, 652 is 1.
HCF(413, 652) = 1
HCF of 413, 652 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, 652 is 1.
Highest Common Factor of 413,652 is 1
Step 1: Since 652 > 413, we apply the division lemma to 652 and 413, to get
652 = 413 x 1 + 239
Step 2: Since the reminder 413 ≠ 0, we apply division lemma to 239 and 413, to get
413 = 239 x 1 + 174
Step 3: We consider the new divisor 239 and the new remainder 174, and apply the division lemma to get
239 = 174 x 1 + 65
We consider the new divisor 174 and the new remainder 65,and apply the division lemma to get
174 = 65 x 2 + 44
We consider the new divisor 65 and the new remainder 44,and apply the division lemma to get
65 = 44 x 1 + 21
We consider the new divisor 44 and the new remainder 21,and apply the division lemma to get
44 = 21 x 2 + 2
We consider the new divisor 21 and the new remainder 2,and apply the division lemma to get
21 = 2 x 10 + 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 652 is 1
Notice that 1 = HCF(2,1) = HCF(21,2) = HCF(44,21) = HCF(65,44) = HCF(174,65) = HCF(239,174) = HCF(413,239) = HCF(652,413) .
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Frequently Asked Questions on HCF of 413, 652 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, 652?
Answer: HCF of 413, 652 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 413, 652 using Euclid's Algorithm?
Answer: For arbitrary numbers 413, 652 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.