Highest Common Factor of 316, 806, 609 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 316, 806, 609 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 316, 806, 609 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 316, 806, 609 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 316, 806, 609 is 1.
HCF(316, 806, 609) = 1
HCF of 316, 806, 609 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 316, 806, 609 is 1.
Highest Common Factor of 316,806,609 is 1
Step 1: Since 806 > 316, we apply the division lemma to 806 and 316, to get
806 = 316 x 2 + 174
Step 2: Since the reminder 316 ≠ 0, we apply division lemma to 174 and 316, to get
316 = 174 x 1 + 142
Step 3: We consider the new divisor 174 and the new remainder 142, and apply the division lemma to get
174 = 142 x 1 + 32
We consider the new divisor 142 and the new remainder 32,and apply the division lemma to get
142 = 32 x 4 + 14
We consider the new divisor 32 and the new remainder 14,and apply the division lemma to get
32 = 14 x 2 + 4
We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get
14 = 4 x 3 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 316 and 806 is 2
Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(32,14) = HCF(142,32) = HCF(174,142) = HCF(316,174) = HCF(806,316) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 609 > 2, we apply the division lemma to 609 and 2, to get
609 = 2 x 304 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 609 is 1
Notice that 1 = HCF(2,1) = HCF(609,2) .
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Frequently Asked Questions on HCF of 316, 806, 609 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 316, 806, 609?
Answer: HCF of 316, 806, 609 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 316, 806, 609 using Euclid's Algorithm?
Answer: For arbitrary numbers 316, 806, 609 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.