Highest Common Factor of 5605, 8142 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 5605, 8142 i.e. 59 the largest integer that leaves a remainder zero for all numbers.
HCF of 5605, 8142 is 59 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 5605, 8142 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 5605, 8142 is 59.
HCF(5605, 8142) = 59
HCF of 5605, 8142 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 5605, 8142 is 59.
Highest Common Factor of 5605,8142 is 59
Step 1: Since 8142 > 5605, we apply the division lemma to 8142 and 5605, to get
8142 = 5605 x 1 + 2537
Step 2: Since the reminder 5605 ≠ 0, we apply division lemma to 2537 and 5605, to get
5605 = 2537 x 2 + 531
Step 3: We consider the new divisor 2537 and the new remainder 531, and apply the division lemma to get
2537 = 531 x 4 + 413
We consider the new divisor 531 and the new remainder 413,and apply the division lemma to get
531 = 413 x 1 + 118
We consider the new divisor 413 and the new remainder 118,and apply the division lemma to get
413 = 118 x 3 + 59
We consider the new divisor 118 and the new remainder 59,and apply the division lemma to get
118 = 59 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 59, the HCF of 5605 and 8142 is 59
Notice that 59 = HCF(118,59) = HCF(413,118) = HCF(531,413) = HCF(2537,531) = HCF(5605,2537) = HCF(8142,5605) .
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Frequently Asked Questions on HCF of 5605, 8142 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 5605, 8142?
Answer: HCF of 5605, 8142 is 59 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 5605, 8142 using Euclid's Algorithm?
Answer: For arbitrary numbers 5605, 8142 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.