Highest Common Factor of 638, 110, 61 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, 110, 61 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 638, 110, 61 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, 110, 61 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, 110, 61 is 1.
HCF(638, 110, 61) = 1
HCF of 638, 110, 61 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, 110, 61 is 1.
Highest Common Factor of 638,110,61 is 1
Step 1: Since 638 > 110, we apply the division lemma to 638 and 110, to get
638 = 110 x 5 + 88
Step 2: Since the reminder 110 ≠ 0, we apply division lemma to 88 and 110, to get
110 = 88 x 1 + 22
Step 3: We consider the new divisor 88 and the new remainder 22, and apply the division lemma to get
88 = 22 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 22, the HCF of 638 and 110 is 22
Notice that 22 = HCF(88,22) = HCF(110,88) = HCF(638,110) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 61 > 22, we apply the division lemma to 61 and 22, to get
61 = 22 x 2 + 17
Step 2: Since the reminder 22 ≠ 0, we apply division lemma to 17 and 22, to get
22 = 17 x 1 + 5
Step 3: We consider the new divisor 17 and the new remainder 5, and apply the division lemma to get
17 = 5 x 3 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 22 and 61 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(17,5) = HCF(22,17) = HCF(61,22) .
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Frequently Asked Questions on HCF of 638, 110, 61 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, 110, 61?
Answer: HCF of 638, 110, 61 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 638, 110, 61 using Euclid's Algorithm?
Answer: For arbitrary numbers 638, 110, 61 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.