Highest Common Factor of 278, 422 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, 422 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 278, 422 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 278, 422 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, 422 is 2.
HCF(278, 422) = 2
HCF of 278, 422 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, 422 is 2.
Highest Common Factor of 278,422 is 2
Step 1: Since 422 > 278, we apply the division lemma to 422 and 278, to get
422 = 278 x 1 + 144
Step 2: Since the reminder 278 ≠ 0, we apply division lemma to 144 and 278, to get
278 = 144 x 1 + 134
Step 3: We consider the new divisor 144 and the new remainder 134, and apply the division lemma to get
144 = 134 x 1 + 10
We consider the new divisor 134 and the new remainder 10,and apply the division lemma to get
134 = 10 x 13 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 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 278 and 422 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(134,10) = HCF(144,134) = HCF(278,144) = HCF(422,278) .
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Frequently Asked Questions on HCF of 278, 422 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, 422?
Answer: HCF of 278, 422 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 278, 422 using Euclid's Algorithm?
Answer: For arbitrary numbers 278, 422 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.