Highest Common Factor of 875, 540, 640 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 875, 540, 640 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 875, 540, 640 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 875, 540, 640 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 875, 540, 640 is 5.
HCF(875, 540, 640) = 5
HCF of 875, 540, 640 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 875, 540, 640 is 5.
Highest Common Factor of 875,540,640 is 5
Step 1: Since 875 > 540, we apply the division lemma to 875 and 540, to get
875 = 540 x 1 + 335
Step 2: Since the reminder 540 ≠ 0, we apply division lemma to 335 and 540, to get
540 = 335 x 1 + 205
Step 3: We consider the new divisor 335 and the new remainder 205, and apply the division lemma to get
335 = 205 x 1 + 130
We consider the new divisor 205 and the new remainder 130,and apply the division lemma to get
205 = 130 x 1 + 75
We consider the new divisor 130 and the new remainder 75,and apply the division lemma to get
130 = 75 x 1 + 55
We consider the new divisor 75 and the new remainder 55,and apply the division lemma to get
75 = 55 x 1 + 20
We consider the new divisor 55 and the new remainder 20,and apply the division lemma to get
55 = 20 x 2 + 15
We consider the new divisor 20 and the new remainder 15,and apply the division lemma to get
20 = 15 x 1 + 5
We consider the new divisor 15 and the new remainder 5,and apply the division lemma to get
15 = 5 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 875 and 540 is 5
Notice that 5 = HCF(15,5) = HCF(20,15) = HCF(55,20) = HCF(75,55) = HCF(130,75) = HCF(205,130) = HCF(335,205) = HCF(540,335) = HCF(875,540) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 640 > 5, we apply the division lemma to 640 and 5, to get
640 = 5 x 128 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 640 is 5
Notice that 5 = HCF(640,5) .
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Frequently Asked Questions on HCF of 875, 540, 640 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 875, 540, 640?
Answer: HCF of 875, 540, 640 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 875, 540, 640 using Euclid's Algorithm?
Answer: For arbitrary numbers 875, 540, 640 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.