Highest Common Factor of 7146, 7893, 15915 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 7146, 7893, 15915 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 7146, 7893, 15915 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 7146, 7893, 15915 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 7146, 7893, 15915 is 3.
HCF(7146, 7893, 15915) = 3
HCF of 7146, 7893, 15915 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7146, 7893, 15915 is 3.
Highest Common Factor of 7146,7893,15915 is 3
Step 1: Since 7893 > 7146, we apply the division lemma to 7893 and 7146, to get
7893 = 7146 x 1 + 747
Step 2: Since the reminder 7146 ≠ 0, we apply division lemma to 747 and 7146, to get
7146 = 747 x 9 + 423
Step 3: We consider the new divisor 747 and the new remainder 423, and apply the division lemma to get
747 = 423 x 1 + 324
We consider the new divisor 423 and the new remainder 324,and apply the division lemma to get
423 = 324 x 1 + 99
We consider the new divisor 324 and the new remainder 99,and apply the division lemma to get
324 = 99 x 3 + 27
We consider the new divisor 99 and the new remainder 27,and apply the division lemma to get
99 = 27 x 3 + 18
We consider the new divisor 27 and the new remainder 18,and apply the division lemma to get
27 = 18 x 1 + 9
We consider the new divisor 18 and the new remainder 9,and apply the division lemma to get
18 = 9 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 7146 and 7893 is 9
Notice that 9 = HCF(18,9) = HCF(27,18) = HCF(99,27) = HCF(324,99) = HCF(423,324) = HCF(747,423) = HCF(7146,747) = HCF(7893,7146) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 15915 > 9, we apply the division lemma to 15915 and 9, to get
15915 = 9 x 1768 + 3
Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 3 and 9, to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 9 and 15915 is 3
Notice that 3 = HCF(9,3) = HCF(15915,9) .
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Frequently Asked Questions on HCF of 7146, 7893, 15915 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 7146, 7893, 15915?
Answer: HCF of 7146, 7893, 15915 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7146, 7893, 15915 using Euclid's Algorithm?
Answer: For arbitrary numbers 7146, 7893, 15915 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.