Highest Common Factor of 296, 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 296, 422 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 296, 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 296, 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 296, 422 is 2.
HCF(296, 422) = 2
HCF of 296, 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 296, 422 is 2.
Highest Common Factor of 296,422 is 2
Step 1: Since 422 > 296, we apply the division lemma to 422 and 296, to get
422 = 296 x 1 + 126
Step 2: Since the reminder 296 ≠ 0, we apply division lemma to 126 and 296, to get
296 = 126 x 2 + 44
Step 3: We consider the new divisor 126 and the new remainder 44, and apply the division lemma to get
126 = 44 x 2 + 38
We consider the new divisor 44 and the new remainder 38,and apply the division lemma to get
44 = 38 x 1 + 6
We consider the new divisor 38 and the new remainder 6,and apply the division lemma to get
38 = 6 x 6 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 296 and 422 is 2
Notice that 2 = HCF(6,2) = HCF(38,6) = HCF(44,38) = HCF(126,44) = HCF(296,126) = HCF(422,296) .
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Frequently Asked Questions on HCF of 296, 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 296, 422?
Answer: HCF of 296, 422 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 296, 422 using Euclid's Algorithm?
Answer: For arbitrary numbers 296, 422 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.