Highest Common Factor of 874, 540 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 874, 540 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 874, 540 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 874, 540 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 874, 540 is 2.
HCF(874, 540) = 2
HCF of 874, 540 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 874, 540 is 2.
Highest Common Factor of 874,540 is 2
Step 1: Since 874 > 540, we apply the division lemma to 874 and 540, to get
874 = 540 x 1 + 334
Step 2: Since the reminder 540 ≠ 0, we apply division lemma to 334 and 540, to get
540 = 334 x 1 + 206
Step 3: We consider the new divisor 334 and the new remainder 206, and apply the division lemma to get
334 = 206 x 1 + 128
We consider the new divisor 206 and the new remainder 128,and apply the division lemma to get
206 = 128 x 1 + 78
We consider the new divisor 128 and the new remainder 78,and apply the division lemma to get
128 = 78 x 1 + 50
We consider the new divisor 78 and the new remainder 50,and apply the division lemma to get
78 = 50 x 1 + 28
We consider the new divisor 50 and the new remainder 28,and apply the division lemma to get
50 = 28 x 1 + 22
We consider the new divisor 28 and the new remainder 22,and apply the division lemma to get
28 = 22 x 1 + 6
We consider the new divisor 22 and the new remainder 6,and apply the division lemma to get
22 = 6 x 3 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma 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 874 and 540 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(22,6) = HCF(28,22) = HCF(50,28) = HCF(78,50) = HCF(128,78) = HCF(206,128) = HCF(334,206) = HCF(540,334) = HCF(874,540) .
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Frequently Asked Questions on HCF of 874, 540 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 874, 540?
Answer: HCF of 874, 540 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 874, 540 using Euclid's Algorithm?
Answer: For arbitrary numbers 874, 540 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.