Highest Common Factor of 565, 12171 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 565, 12171 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 565, 12171 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 565, 12171 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 565, 12171 is 1.
HCF(565, 12171) = 1
HCF of 565, 12171 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 565, 12171 is 1.
Highest Common Factor of 565,12171 is 1
Step 1: Since 12171 > 565, we apply the division lemma to 12171 and 565, to get
12171 = 565 x 21 + 306
Step 2: Since the reminder 565 ≠ 0, we apply division lemma to 306 and 565, to get
565 = 306 x 1 + 259
Step 3: We consider the new divisor 306 and the new remainder 259, and apply the division lemma to get
306 = 259 x 1 + 47
We consider the new divisor 259 and the new remainder 47,and apply the division lemma to get
259 = 47 x 5 + 24
We consider the new divisor 47 and the new remainder 24,and apply the division lemma to get
47 = 24 x 1 + 23
We consider the new divisor 24 and the new remainder 23,and apply the division lemma to get
24 = 23 x 1 + 1
We consider the new divisor 23 and the new remainder 1,and apply the division lemma to get
23 = 1 x 23 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 565 and 12171 is 1
Notice that 1 = HCF(23,1) = HCF(24,23) = HCF(47,24) = HCF(259,47) = HCF(306,259) = HCF(565,306) = HCF(12171,565) .
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Frequently Asked Questions on HCF of 565, 12171 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 565, 12171?
Answer: HCF of 565, 12171 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 565, 12171 using Euclid's Algorithm?
Answer: For arbitrary numbers 565, 12171 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.