Highest Common Factor of 540, 680, 873, 54 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, 680, 873, 54 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 540, 680, 873, 54 is 1 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, 680, 873, 54 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, 680, 873, 54 is 1.
HCF(540, 680, 873, 54) = 1
HCF of 540, 680, 873, 54 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, 680, 873, 54 is 1.
Highest Common Factor of 540,680,873,54 is 1
Step 1: Since 680 > 540, we apply the division lemma to 680 and 540, to get
680 = 540 x 1 + 140
Step 2: Since the reminder 540 ≠ 0, we apply division lemma to 140 and 540, to get
540 = 140 x 3 + 120
Step 3: We consider the new divisor 140 and the new remainder 120, and apply the division lemma to get
140 = 120 x 1 + 20
We consider the new divisor 120 and the new remainder 20, and apply the division lemma to get
120 = 20 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 540 and 680 is 20
Notice that 20 = HCF(120,20) = HCF(140,120) = HCF(540,140) = HCF(680,540) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 873 > 20, we apply the division lemma to 873 and 20, to get
873 = 20 x 43 + 13
Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 13 and 20, to get
20 = 13 x 1 + 7
Step 3: We consider the new divisor 13 and the new remainder 7, and apply the division lemma to get
13 = 7 x 1 + 6
We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get
7 = 6 x 1 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 20 and 873 is 1
Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(13,7) = HCF(20,13) = HCF(873,20) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 54 > 1, we apply the division lemma to 54 and 1, to get
54 = 1 x 54 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 54 is 1
Notice that 1 = HCF(54,1) .
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Frequently Asked Questions on HCF of 540, 680, 873, 54 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, 680, 873, 54?
Answer: HCF of 540, 680, 873, 54 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 540, 680, 873, 54 using Euclid's Algorithm?
Answer: For arbitrary numbers 540, 680, 873, 54 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
