Highest Common Factor of 865, 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 865, 540 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 865, 540 is 5 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 865, 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 865, 540 is 5.
HCF(865, 540) = 5
HCF of 865, 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 865, 540 is 5.
Highest Common Factor of 865,540 is 5
Step 1: Since 865 > 540, we apply the division lemma to 865 and 540, to get
865 = 540 x 1 + 325
Step 2: Since the reminder 540 ≠ 0, we apply division lemma to 325 and 540, to get
540 = 325 x 1 + 215
Step 3: We consider the new divisor 325 and the new remainder 215, and apply the division lemma to get
325 = 215 x 1 + 110
We consider the new divisor 215 and the new remainder 110,and apply the division lemma to get
215 = 110 x 1 + 105
We consider the new divisor 110 and the new remainder 105,and apply the division lemma to get
110 = 105 x 1 + 5
We consider the new divisor 105 and the new remainder 5,and apply the division lemma to get
105 = 5 x 21 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 865 and 540 is 5
Notice that 5 = HCF(105,5) = HCF(110,105) = HCF(215,110) = HCF(325,215) = HCF(540,325) = HCF(865,540) .
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Frequently Asked Questions on HCF of 865, 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 865, 540?
Answer: HCF of 865, 540 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 865, 540 using Euclid's Algorithm?
Answer: For arbitrary numbers 865, 540 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.