Highest Common Factor of 316, 512, 590 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, 512, 590 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 316, 512, 590 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 316, 512, 590 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, 512, 590 is 2.
HCF(316, 512, 590) = 2
HCF of 316, 512, 590 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, 512, 590 is 2.
Highest Common Factor of 316,512,590 is 2
Step 1: Since 512 > 316, we apply the division lemma to 512 and 316, to get
512 = 316 x 1 + 196
Step 2: Since the reminder 316 ≠ 0, we apply division lemma to 196 and 316, to get
316 = 196 x 1 + 120
Step 3: We consider the new divisor 196 and the new remainder 120, and apply the division lemma to get
196 = 120 x 1 + 76
We consider the new divisor 120 and the new remainder 76,and apply the division lemma to get
120 = 76 x 1 + 44
We consider the new divisor 76 and the new remainder 44,and apply the division lemma to get
76 = 44 x 1 + 32
We consider the new divisor 44 and the new remainder 32,and apply the division lemma to get
44 = 32 x 1 + 12
We consider the new divisor 32 and the new remainder 12,and apply the division lemma to get
32 = 12 x 2 + 8
We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get
12 = 8 x 1 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 316 and 512 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(32,12) = HCF(44,32) = HCF(76,44) = HCF(120,76) = HCF(196,120) = HCF(316,196) = HCF(512,316) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 590 > 4, we apply the division lemma to 590 and 4, to get
590 = 4 x 147 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, 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 4 and 590 is 2
Notice that 2 = HCF(4,2) = HCF(590,4) .
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Frequently Asked Questions on HCF of 316, 512, 590 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, 512, 590?
Answer: HCF of 316, 512, 590 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 316, 512, 590 using Euclid's Algorithm?
Answer: For arbitrary numbers 316, 512, 590 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.