Highest Common Factor of 582, 885, 921 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 582, 885, 921 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 582, 885, 921 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 582, 885, 921 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 582, 885, 921 is 3.
HCF(582, 885, 921) = 3
HCF of 582, 885, 921 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 582, 885, 921 is 3.
Highest Common Factor of 582,885,921 is 3
Step 1: Since 885 > 582, we apply the division lemma to 885 and 582, to get
885 = 582 x 1 + 303
Step 2: Since the reminder 582 ≠ 0, we apply division lemma to 303 and 582, to get
582 = 303 x 1 + 279
Step 3: We consider the new divisor 303 and the new remainder 279, and apply the division lemma to get
303 = 279 x 1 + 24
We consider the new divisor 279 and the new remainder 24,and apply the division lemma to get
279 = 24 x 11 + 15
We consider the new divisor 24 and the new remainder 15,and apply the division lemma to get
24 = 15 x 1 + 9
We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get
15 = 9 x 1 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 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 582 and 885 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(24,15) = HCF(279,24) = HCF(303,279) = HCF(582,303) = HCF(885,582) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 921 > 3, we apply the division lemma to 921 and 3, to get
921 = 3 x 307 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 921 is 3
Notice that 3 = HCF(921,3) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 582, 885, 921 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 582, 885, 921?
Answer: HCF of 582, 885, 921 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 582, 885, 921 using Euclid's Algorithm?
Answer: For arbitrary numbers 582, 885, 921 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.