Highest Common Factor of 2514, 3912, 38700 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 2514, 3912, 38700 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 2514, 3912, 38700 is 6 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 2514, 3912, 38700 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 2514, 3912, 38700 is 6.
HCF(2514, 3912, 38700) = 6
HCF of 2514, 3912, 38700 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2514, 3912, 38700 is 6.
Highest Common Factor of 2514,3912,38700 is 6
Step 1: Since 3912 > 2514, we apply the division lemma to 3912 and 2514, to get
3912 = 2514 x 1 + 1398
Step 2: Since the reminder 2514 ≠ 0, we apply division lemma to 1398 and 2514, to get
2514 = 1398 x 1 + 1116
Step 3: We consider the new divisor 1398 and the new remainder 1116, and apply the division lemma to get
1398 = 1116 x 1 + 282
We consider the new divisor 1116 and the new remainder 282,and apply the division lemma to get
1116 = 282 x 3 + 270
We consider the new divisor 282 and the new remainder 270,and apply the division lemma to get
282 = 270 x 1 + 12
We consider the new divisor 270 and the new remainder 12,and apply the division lemma to get
270 = 12 x 22 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 2514 and 3912 is 6
Notice that 6 = HCF(12,6) = HCF(270,12) = HCF(282,270) = HCF(1116,282) = HCF(1398,1116) = HCF(2514,1398) = HCF(3912,2514) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 38700 > 6, we apply the division lemma to 38700 and 6, to get
38700 = 6 x 6450 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 6 and 38700 is 6
Notice that 6 = HCF(38700,6) .
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Frequently Asked Questions on HCF of 2514, 3912, 38700 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 2514, 3912, 38700?
Answer: HCF of 2514, 3912, 38700 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2514, 3912, 38700 using Euclid's Algorithm?
Answer: For arbitrary numbers 2514, 3912, 38700 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.