Highest Common Factor of 2574, 6108 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 2574, 6108 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 2574, 6108 is 6 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 2574, 6108 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 2574, 6108 is 6.
HCF(2574, 6108) = 6
HCF of 2574, 6108 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2574, 6108 is 6.
Highest Common Factor of 2574,6108 is 6
Step 1: Since 6108 > 2574, we apply the division lemma to 6108 and 2574, to get
6108 = 2574 x 2 + 960
Step 2: Since the reminder 2574 ≠ 0, we apply division lemma to 960 and 2574, to get
2574 = 960 x 2 + 654
Step 3: We consider the new divisor 960 and the new remainder 654, and apply the division lemma to get
960 = 654 x 1 + 306
We consider the new divisor 654 and the new remainder 306,and apply the division lemma to get
654 = 306 x 2 + 42
We consider the new divisor 306 and the new remainder 42,and apply the division lemma to get
306 = 42 x 7 + 12
We consider the new divisor 42 and the new remainder 12,and apply the division lemma to get
42 = 12 x 3 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 2574 and 6108 is 6
Notice that 6 = HCF(12,6) = HCF(42,12) = HCF(306,42) = HCF(654,306) = HCF(960,654) = HCF(2574,960) = HCF(6108,2574) .
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Frequently Asked Questions on HCF of 2574, 6108 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 2574, 6108?
Answer: HCF of 2574, 6108 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2574, 6108 using Euclid's Algorithm?
Answer: For arbitrary numbers 2574, 6108 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.