Highest Common Factor of 518, 306, 698 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 518, 306, 698 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 518, 306, 698 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 518, 306, 698 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 518, 306, 698 is 2.
HCF(518, 306, 698) = 2
HCF of 518, 306, 698 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 518, 306, 698 is 2.
Highest Common Factor of 518,306,698 is 2
Step 1: Since 518 > 306, we apply the division lemma to 518 and 306, to get
518 = 306 x 1 + 212
Step 2: Since the reminder 306 ≠ 0, we apply division lemma to 212 and 306, to get
306 = 212 x 1 + 94
Step 3: We consider the new divisor 212 and the new remainder 94, and apply the division lemma to get
212 = 94 x 2 + 24
We consider the new divisor 94 and the new remainder 24,and apply the division lemma to get
94 = 24 x 3 + 22
We consider the new divisor 24 and the new remainder 22,and apply the division lemma to get
24 = 22 x 1 + 2
We consider the new divisor 22 and the new remainder 2,and apply the division lemma to get
22 = 2 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 518 and 306 is 2
Notice that 2 = HCF(22,2) = HCF(24,22) = HCF(94,24) = HCF(212,94) = HCF(306,212) = HCF(518,306) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 698 > 2, we apply the division lemma to 698 and 2, to get
698 = 2 x 349 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 698 is 2
Notice that 2 = HCF(698,2) .
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Frequently Asked Questions on HCF of 518, 306, 698 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 518, 306, 698?
Answer: HCF of 518, 306, 698 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 518, 306, 698 using Euclid's Algorithm?
Answer: For arbitrary numbers 518, 306, 698 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.