Highest Common Factor of 278, 209, 978, 217 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, 209, 978, 217 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 278, 209, 978, 217 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, 209, 978, 217 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, 209, 978, 217 is 1.
HCF(278, 209, 978, 217) = 1
HCF of 278, 209, 978, 217 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, 209, 978, 217 is 1.
Highest Common Factor of 278,209,978,217 is 1
Step 1: Since 278 > 209, we apply the division lemma to 278 and 209, to get
278 = 209 x 1 + 69
Step 2: Since the reminder 209 ≠ 0, we apply division lemma to 69 and 209, to get
209 = 69 x 3 + 2
Step 3: We consider the new divisor 69 and the new remainder 2, and apply the division lemma to get
69 = 2 x 34 + 1
We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 278 and 209 is 1
Notice that 1 = HCF(2,1) = HCF(69,2) = HCF(209,69) = HCF(278,209) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 978 > 1, we apply the division lemma to 978 and 1, to get
978 = 1 x 978 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 978 is 1
Notice that 1 = HCF(978,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 217 > 1, we apply the division lemma to 217 and 1, to get
217 = 1 x 217 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 217 is 1
Notice that 1 = HCF(217,1) .
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Frequently Asked Questions on HCF of 278, 209, 978, 217 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, 209, 978, 217?
Answer: HCF of 278, 209, 978, 217 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 278, 209, 978, 217 using Euclid's Algorithm?
Answer: For arbitrary numbers 278, 209, 978, 217 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.