Highest Common Factor of 663, 422, 458 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 663, 422, 458 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 663, 422, 458 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 663, 422, 458 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 663, 422, 458 is 1.
HCF(663, 422, 458) = 1
HCF of 663, 422, 458 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 663, 422, 458 is 1.
Highest Common Factor of 663,422,458 is 1
Step 1: Since 663 > 422, we apply the division lemma to 663 and 422, to get
663 = 422 x 1 + 241
Step 2: Since the reminder 422 ≠ 0, we apply division lemma to 241 and 422, to get
422 = 241 x 1 + 181
Step 3: We consider the new divisor 241 and the new remainder 181, and apply the division lemma to get
241 = 181 x 1 + 60
We consider the new divisor 181 and the new remainder 60,and apply the division lemma to get
181 = 60 x 3 + 1
We consider the new divisor 60 and the new remainder 1,and apply the division lemma to get
60 = 1 x 60 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 663 and 422 is 1
Notice that 1 = HCF(60,1) = HCF(181,60) = HCF(241,181) = HCF(422,241) = HCF(663,422) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 458 > 1, we apply the division lemma to 458 and 1, to get
458 = 1 x 458 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 458 is 1
Notice that 1 = HCF(458,1) .
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Frequently Asked Questions on HCF of 663, 422, 458 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 663, 422, 458?
Answer: HCF of 663, 422, 458 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 663, 422, 458 using Euclid's Algorithm?
Answer: For arbitrary numbers 663, 422, 458 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.