Highest Common Factor of 540, 8421 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 540, 8421 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 540, 8421 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 540, 8421 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 540, 8421 is 3.
HCF(540, 8421) = 3
HCF of 540, 8421 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 540, 8421 is 3.
Highest Common Factor of 540,8421 is 3
Step 1: Since 8421 > 540, we apply the division lemma to 8421 and 540, to get
8421 = 540 x 15 + 321
Step 2: Since the reminder 540 ≠ 0, we apply division lemma to 321 and 540, to get
540 = 321 x 1 + 219
Step 3: We consider the new divisor 321 and the new remainder 219, and apply the division lemma to get
321 = 219 x 1 + 102
We consider the new divisor 219 and the new remainder 102,and apply the division lemma to get
219 = 102 x 2 + 15
We consider the new divisor 102 and the new remainder 15,and apply the division lemma to get
102 = 15 x 6 + 12
We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get
15 = 12 x 1 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 540 and 8421 is 3
Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(102,15) = HCF(219,102) = HCF(321,219) = HCF(540,321) = HCF(8421,540) .
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Frequently Asked Questions on HCF of 540, 8421 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 540, 8421?
Answer: HCF of 540, 8421 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 540, 8421 using Euclid's Algorithm?
Answer: For arbitrary numbers 540, 8421 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.