Highest Common Factor of 3660, 7866, 21572 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 3660, 7866, 21572 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 3660, 7866, 21572 is 2 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 3660, 7866, 21572 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 3660, 7866, 21572 is 2.
HCF(3660, 7866, 21572) = 2
HCF of 3660, 7866, 21572 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3660, 7866, 21572 is 2.
Highest Common Factor of 3660,7866,21572 is 2
Step 1: Since 7866 > 3660, we apply the division lemma to 7866 and 3660, to get
7866 = 3660 x 2 + 546
Step 2: Since the reminder 3660 ≠ 0, we apply division lemma to 546 and 3660, to get
3660 = 546 x 6 + 384
Step 3: We consider the new divisor 546 and the new remainder 384, and apply the division lemma to get
546 = 384 x 1 + 162
We consider the new divisor 384 and the new remainder 162,and apply the division lemma to get
384 = 162 x 2 + 60
We consider the new divisor 162 and the new remainder 60,and apply the division lemma to get
162 = 60 x 2 + 42
We consider the new divisor 60 and the new remainder 42,and apply the division lemma to get
60 = 42 x 1 + 18
We consider the new divisor 42 and the new remainder 18,and apply the division lemma to get
42 = 18 x 2 + 6
We consider the new divisor 18 and the new remainder 6,and apply the division lemma to get
18 = 6 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 3660 and 7866 is 6
Notice that 6 = HCF(18,6) = HCF(42,18) = HCF(60,42) = HCF(162,60) = HCF(384,162) = HCF(546,384) = HCF(3660,546) = HCF(7866,3660) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 21572 > 6, we apply the division lemma to 21572 and 6, to get
21572 = 6 x 3595 + 2
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 2 and 6, to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6 and 21572 is 2
Notice that 2 = HCF(6,2) = HCF(21572,6) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 3660, 7866, 21572 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 3660, 7866, 21572?
Answer: HCF of 3660, 7866, 21572 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3660, 7866, 21572 using Euclid's Algorithm?
Answer: For arbitrary numbers 3660, 7866, 21572 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.