Highest Common Factor of 798, 312, 518 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 798, 312, 518 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 798, 312, 518 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 798, 312, 518 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 798, 312, 518 is 2.
HCF(798, 312, 518) = 2
HCF of 798, 312, 518 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 798, 312, 518 is 2.
Highest Common Factor of 798,312,518 is 2
Step 1: Since 798 > 312, we apply the division lemma to 798 and 312, to get
798 = 312 x 2 + 174
Step 2: Since the reminder 312 ≠ 0, we apply division lemma to 174 and 312, to get
312 = 174 x 1 + 138
Step 3: We consider the new divisor 174 and the new remainder 138, and apply the division lemma to get
174 = 138 x 1 + 36
We consider the new divisor 138 and the new remainder 36,and apply the division lemma to get
138 = 36 x 3 + 30
We consider the new divisor 36 and the new remainder 30,and apply the division lemma to get
36 = 30 x 1 + 6
We consider the new divisor 30 and the new remainder 6,and apply the division lemma to get
30 = 6 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 798 and 312 is 6
Notice that 6 = HCF(30,6) = HCF(36,30) = HCF(138,36) = HCF(174,138) = HCF(312,174) = HCF(798,312) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 518 > 6, we apply the division lemma to 518 and 6, to get
518 = 6 x 86 + 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 518 is 2
Notice that 2 = HCF(6,2) = HCF(518,6) .
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Frequently Asked Questions on HCF of 798, 312, 518 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 798, 312, 518?
Answer: HCF of 798, 312, 518 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 798, 312, 518 using Euclid's Algorithm?
Answer: For arbitrary numbers 798, 312, 518 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.