Highest Common Factor of 540, 864 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, 864 i.e. 108 the largest integer that leaves a remainder zero for all numbers.
HCF of 540, 864 is 108 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, 864 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, 864 is 108.
HCF(540, 864) = 108
HCF of 540, 864 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, 864 is 108.
Highest Common Factor of 540,864 is 108
Step 1: Since 864 > 540, we apply the division lemma to 864 and 540, to get
864 = 540 x 1 + 324
Step 2: Since the reminder 540 ≠ 0, we apply division lemma to 324 and 540, to get
540 = 324 x 1 + 216
Step 3: We consider the new divisor 324 and the new remainder 216, and apply the division lemma to get
324 = 216 x 1 + 108
We consider the new divisor 216 and the new remainder 108, and apply the division lemma to get
216 = 108 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 108, the HCF of 540 and 864 is 108
Notice that 108 = HCF(216,108) = HCF(324,216) = HCF(540,324) = HCF(864,540) .
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Frequently Asked Questions on HCF of 540, 864 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, 864?
Answer: HCF of 540, 864 is 108 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 540, 864 using Euclid's Algorithm?
Answer: For arbitrary numbers 540, 864 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.