Highest Common Factor of 852, 561 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 852, 561 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 852, 561 is 3 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 852, 561 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 852, 561 is 3.
HCF(852, 561) = 3
HCF of 852, 561 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 852, 561 is 3.
Highest Common Factor of 852,561 is 3
Step 1: Since 852 > 561, we apply the division lemma to 852 and 561, to get
852 = 561 x 1 + 291
Step 2: Since the reminder 561 ≠ 0, we apply division lemma to 291 and 561, to get
561 = 291 x 1 + 270
Step 3: We consider the new divisor 291 and the new remainder 270, and apply the division lemma to get
291 = 270 x 1 + 21
We consider the new divisor 270 and the new remainder 21,and apply the division lemma to get
270 = 21 x 12 + 18
We consider the new divisor 21 and the new remainder 18,and apply the division lemma to get
21 = 18 x 1 + 3
We consider the new divisor 18 and the new remainder 3,and apply the division lemma to get
18 = 3 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 852 and 561 is 3
Notice that 3 = HCF(18,3) = HCF(21,18) = HCF(270,21) = HCF(291,270) = HCF(561,291) = HCF(852,561) .
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Frequently Asked Questions on HCF of 852, 561 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 852, 561?
Answer: HCF of 852, 561 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 852, 561 using Euclid's Algorithm?
Answer: For arbitrary numbers 852, 561 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
