Highest Common Factor of 618, 878, 51 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 618, 878, 51 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 618, 878, 51 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 618, 878, 51 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 618, 878, 51 is 1.
HCF(618, 878, 51) = 1
HCF of 618, 878, 51 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 618, 878, 51 is 1.
Highest Common Factor of 618,878,51 is 1
Step 1: Since 878 > 618, we apply the division lemma to 878 and 618, to get
878 = 618 x 1 + 260
Step 2: Since the reminder 618 ≠ 0, we apply division lemma to 260 and 618, to get
618 = 260 x 2 + 98
Step 3: We consider the new divisor 260 and the new remainder 98, and apply the division lemma to get
260 = 98 x 2 + 64
We consider the new divisor 98 and the new remainder 64,and apply the division lemma to get
98 = 64 x 1 + 34
We consider the new divisor 64 and the new remainder 34,and apply the division lemma to get
64 = 34 x 1 + 30
We consider the new divisor 34 and the new remainder 30,and apply the division lemma to get
34 = 30 x 1 + 4
We consider the new divisor 30 and the new remainder 4,and apply the division lemma to get
30 = 4 x 7 + 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 618 and 878 is 2
Notice that 2 = HCF(4,2) = HCF(30,4) = HCF(34,30) = HCF(64,34) = HCF(98,64) = HCF(260,98) = HCF(618,260) = HCF(878,618) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 51 > 2, we apply the division lemma to 51 and 2, to get
51 = 2 x 25 + 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 51 is 1
Notice that 1 = HCF(2,1) = HCF(51,2) .
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Frequently Asked Questions on HCF of 618, 878, 51 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 618, 878, 51?
Answer: HCF of 618, 878, 51 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 618, 878, 51 using Euclid's Algorithm?
Answer: For arbitrary numbers 618, 878, 51 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
