Highest Common Factor of 721, 618, 278 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 721, 618, 278 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 721, 618, 278 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 721, 618, 278 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 721, 618, 278 is 1.
HCF(721, 618, 278) = 1
HCF of 721, 618, 278 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 721, 618, 278 is 1.
Highest Common Factor of 721,618,278 is 1
Step 1: Since 721 > 618, we apply the division lemma to 721 and 618, to get
721 = 618 x 1 + 103
Step 2: Since the reminder 618 ≠ 0, we apply division lemma to 103 and 618, to get
618 = 103 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 103, the HCF of 721 and 618 is 103
Notice that 103 = HCF(618,103) = HCF(721,618) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 278 > 103, we apply the division lemma to 278 and 103, to get
278 = 103 x 2 + 72
Step 2: Since the reminder 103 ≠ 0, we apply division lemma to 72 and 103, to get
103 = 72 x 1 + 31
Step 3: We consider the new divisor 72 and the new remainder 31, and apply the division lemma to get
72 = 31 x 2 + 10
We consider the new divisor 31 and the new remainder 10,and apply the division lemma to get
31 = 10 x 3 + 1
We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 103 and 278 is 1
Notice that 1 = HCF(10,1) = HCF(31,10) = HCF(72,31) = HCF(103,72) = HCF(278,103) .
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Frequently Asked Questions on HCF of 721, 618, 278 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 721, 618, 278?
Answer: HCF of 721, 618, 278 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 721, 618, 278 using Euclid's Algorithm?
Answer: For arbitrary numbers 721, 618, 278 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
