Highest Common Factor of 572, 852, 874 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 572, 852, 874 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 572, 852, 874 is 2 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 572, 852, 874 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 572, 852, 874 is 2.
HCF(572, 852, 874) = 2
HCF of 572, 852, 874 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 572, 852, 874 is 2.
Highest Common Factor of 572,852,874 is 2
Step 1: Since 852 > 572, we apply the division lemma to 852 and 572, to get
852 = 572 x 1 + 280
Step 2: Since the reminder 572 ≠ 0, we apply division lemma to 280 and 572, to get
572 = 280 x 2 + 12
Step 3: We consider the new divisor 280 and the new remainder 12, and apply the division lemma to get
280 = 12 x 23 + 4
We consider the new divisor 12 and the new remainder 4, and apply the division lemma to get
12 = 4 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 572 and 852 is 4
Notice that 4 = HCF(12,4) = HCF(280,12) = HCF(572,280) = HCF(852,572) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 874 > 4, we apply the division lemma to 874 and 4, to get
874 = 4 x 218 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4 and 874 is 2
Notice that 2 = HCF(4,2) = HCF(874,4) .
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Frequently Asked Questions on HCF of 572, 852, 874 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 572, 852, 874?
Answer: HCF of 572, 852, 874 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 572, 852, 874 using Euclid's Algorithm?
Answer: For arbitrary numbers 572, 852, 874 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.