Highest Common Factor of 309, 586, 872 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 309, 586, 872 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 309, 586, 872 is 1 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 309, 586, 872 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 309, 586, 872 is 1.
HCF(309, 586, 872) = 1
HCF of 309, 586, 872 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 309, 586, 872 is 1.
Highest Common Factor of 309,586,872 is 1
Step 1: Since 586 > 309, we apply the division lemma to 586 and 309, to get
586 = 309 x 1 + 277
Step 2: Since the reminder 309 ≠ 0, we apply division lemma to 277 and 309, to get
309 = 277 x 1 + 32
Step 3: We consider the new divisor 277 and the new remainder 32, and apply the division lemma to get
277 = 32 x 8 + 21
We consider the new divisor 32 and the new remainder 21,and apply the division lemma to get
32 = 21 x 1 + 11
We consider the new divisor 21 and the new remainder 11,and apply the division lemma to get
21 = 11 x 1 + 10
We consider the new divisor 11 and the new remainder 10,and apply the division lemma to get
11 = 10 x 1 + 1
We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 309 and 586 is 1
Notice that 1 = HCF(10,1) = HCF(11,10) = HCF(21,11) = HCF(32,21) = HCF(277,32) = HCF(309,277) = HCF(586,309) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 872 > 1, we apply the division lemma to 872 and 1, to get
872 = 1 x 872 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 872 is 1
Notice that 1 = HCF(872,1) .
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Frequently Asked Questions on HCF of 309, 586, 872 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 309, 586, 872?
Answer: HCF of 309, 586, 872 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 309, 586, 872 using Euclid's Algorithm?
Answer: For arbitrary numbers 309, 586, 872 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
