Highest Common Factor of 3138, 5739, 21225 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 3138, 5739, 21225 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 3138, 5739, 21225 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 3138, 5739, 21225 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 3138, 5739, 21225 is 3.
HCF(3138, 5739, 21225) = 3
HCF of 3138, 5739, 21225 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3138, 5739, 21225 is 3.
Highest Common Factor of 3138,5739,21225 is 3
Step 1: Since 5739 > 3138, we apply the division lemma to 5739 and 3138, to get
5739 = 3138 x 1 + 2601
Step 2: Since the reminder 3138 ≠ 0, we apply division lemma to 2601 and 3138, to get
3138 = 2601 x 1 + 537
Step 3: We consider the new divisor 2601 and the new remainder 537, and apply the division lemma to get
2601 = 537 x 4 + 453
We consider the new divisor 537 and the new remainder 453,and apply the division lemma to get
537 = 453 x 1 + 84
We consider the new divisor 453 and the new remainder 84,and apply the division lemma to get
453 = 84 x 5 + 33
We consider the new divisor 84 and the new remainder 33,and apply the division lemma to get
84 = 33 x 2 + 18
We consider the new divisor 33 and the new remainder 18,and apply the division lemma to get
33 = 18 x 1 + 15
We consider the new divisor 18 and the new remainder 15,and apply the division lemma to get
18 = 15 x 1 + 3
We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3138 and 5739 is 3
Notice that 3 = HCF(15,3) = HCF(18,15) = HCF(33,18) = HCF(84,33) = HCF(453,84) = HCF(537,453) = HCF(2601,537) = HCF(3138,2601) = HCF(5739,3138) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 21225 > 3, we apply the division lemma to 21225 and 3, to get
21225 = 3 x 7075 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 21225 is 3
Notice that 3 = HCF(21225,3) .
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Frequently Asked Questions on HCF of 3138, 5739, 21225 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 3138, 5739, 21225?
Answer: HCF of 3138, 5739, 21225 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3138, 5739, 21225 using Euclid's Algorithm?
Answer: For arbitrary numbers 3138, 5739, 21225 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.