Highest Common Factor of 638, 404, 389 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 638, 404, 389 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 638, 404, 389 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 638, 404, 389 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 638, 404, 389 is 1.
HCF(638, 404, 389) = 1
HCF of 638, 404, 389 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 638, 404, 389 is 1.
Highest Common Factor of 638,404,389 is 1
Step 1: Since 638 > 404, we apply the division lemma to 638 and 404, to get
638 = 404 x 1 + 234
Step 2: Since the reminder 404 ≠ 0, we apply division lemma to 234 and 404, to get
404 = 234 x 1 + 170
Step 3: We consider the new divisor 234 and the new remainder 170, and apply the division lemma to get
234 = 170 x 1 + 64
We consider the new divisor 170 and the new remainder 64,and apply the division lemma to get
170 = 64 x 2 + 42
We consider the new divisor 64 and the new remainder 42,and apply the division lemma to get
64 = 42 x 1 + 22
We consider the new divisor 42 and the new remainder 22,and apply the division lemma to get
42 = 22 x 1 + 20
We consider the new divisor 22 and the new remainder 20,and apply the division lemma to get
22 = 20 x 1 + 2
We consider the new divisor 20 and the new remainder 2,and apply the division lemma to get
20 = 2 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 638 and 404 is 2
Notice that 2 = HCF(20,2) = HCF(22,20) = HCF(42,22) = HCF(64,42) = HCF(170,64) = HCF(234,170) = HCF(404,234) = HCF(638,404) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 389 > 2, we apply the division lemma to 389 and 2, to get
389 = 2 x 194 + 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 389 is 1
Notice that 1 = HCF(2,1) = HCF(389,2) .
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Frequently Asked Questions on HCF of 638, 404, 389 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 638, 404, 389?
Answer: HCF of 638, 404, 389 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 638, 404, 389 using Euclid's Algorithm?
Answer: For arbitrary numbers 638, 404, 389 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
