Highest Common Factor of 8160, 6525, 69231 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 8160, 6525, 69231 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 8160, 6525, 69231 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 8160, 6525, 69231 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 8160, 6525, 69231 is 3.
HCF(8160, 6525, 69231) = 3
HCF of 8160, 6525, 69231 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8160, 6525, 69231 is 3.
Highest Common Factor of 8160,6525,69231 is 3
Step 1: Since 8160 > 6525, we apply the division lemma to 8160 and 6525, to get
8160 = 6525 x 1 + 1635
Step 2: Since the reminder 6525 ≠ 0, we apply division lemma to 1635 and 6525, to get
6525 = 1635 x 3 + 1620
Step 3: We consider the new divisor 1635 and the new remainder 1620, and apply the division lemma to get
1635 = 1620 x 1 + 15
We consider the new divisor 1620 and the new remainder 15, and apply the division lemma to get
1620 = 15 x 108 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 8160 and 6525 is 15
Notice that 15 = HCF(1620,15) = HCF(1635,1620) = HCF(6525,1635) = HCF(8160,6525) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 69231 > 15, we apply the division lemma to 69231 and 15, to get
69231 = 15 x 4615 + 6
Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 6 and 15, to get
15 = 6 x 2 + 3
Step 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 15 and 69231 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(69231,15) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 8160, 6525, 69231 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 8160, 6525, 69231?
Answer: HCF of 8160, 6525, 69231 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8160, 6525, 69231 using Euclid's Algorithm?
Answer: For arbitrary numbers 8160, 6525, 69231 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.