Highest Common Factor of 2640, 5091, 51288 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 2640, 5091, 51288 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 2640, 5091, 51288 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 2640, 5091, 51288 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 2640, 5091, 51288 is 3.
HCF(2640, 5091, 51288) = 3
HCF of 2640, 5091, 51288 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2640, 5091, 51288 is 3.
Highest Common Factor of 2640,5091,51288 is 3
Step 1: Since 5091 > 2640, we apply the division lemma to 5091 and 2640, to get
5091 = 2640 x 1 + 2451
Step 2: Since the reminder 2640 ≠ 0, we apply division lemma to 2451 and 2640, to get
2640 = 2451 x 1 + 189
Step 3: We consider the new divisor 2451 and the new remainder 189, and apply the division lemma to get
2451 = 189 x 12 + 183
We consider the new divisor 189 and the new remainder 183,and apply the division lemma to get
189 = 183 x 1 + 6
We consider the new divisor 183 and the new remainder 6,and apply the division lemma to get
183 = 6 x 30 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 2640 and 5091 is 3
Notice that 3 = HCF(6,3) = HCF(183,6) = HCF(189,183) = HCF(2451,189) = HCF(2640,2451) = HCF(5091,2640) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 51288 > 3, we apply the division lemma to 51288 and 3, to get
51288 = 3 x 17096 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 51288 is 3
Notice that 3 = HCF(51288,3) .
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Frequently Asked Questions on HCF of 2640, 5091, 51288 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 2640, 5091, 51288?
Answer: HCF of 2640, 5091, 51288 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2640, 5091, 51288 using Euclid's Algorithm?
Answer: For arbitrary numbers 2640, 5091, 51288 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.