Highest Common Factor of 278, 206, 259 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 278, 206, 259 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 278, 206, 259 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 278, 206, 259 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 278, 206, 259 is 1.
HCF(278, 206, 259) = 1
HCF of 278, 206, 259 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 278, 206, 259 is 1.
Highest Common Factor of 278,206,259 is 1
Step 1: Since 278 > 206, we apply the division lemma to 278 and 206, to get
278 = 206 x 1 + 72
Step 2: Since the reminder 206 ≠ 0, we apply division lemma to 72 and 206, to get
206 = 72 x 2 + 62
Step 3: We consider the new divisor 72 and the new remainder 62, and apply the division lemma to get
72 = 62 x 1 + 10
We consider the new divisor 62 and the new remainder 10,and apply the division lemma to get
62 = 10 x 6 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 278 and 206 is 2
Notice that 2 = HCF(10,2) = HCF(62,10) = HCF(72,62) = HCF(206,72) = HCF(278,206) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 259 > 2, we apply the division lemma to 259 and 2, to get
259 = 2 x 129 + 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 259 is 1
Notice that 1 = HCF(2,1) = HCF(259,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 278, 206, 259 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 278, 206, 259?
Answer: HCF of 278, 206, 259 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 278, 206, 259 using Euclid's Algorithm?
Answer: For arbitrary numbers 278, 206, 259 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.