Highest Common Factor of 218, 138, 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 218, 138, 61 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 218, 138, 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 218, 138, 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 218, 138, 61 is 1.
HCF(218, 138, 61) = 1
HCF of 218, 138, 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 218, 138, 61 is 1.
Highest Common Factor of 218,138,61 is 1
Step 1: Since 218 > 138, we apply the division lemma to 218 and 138, to get
218 = 138 x 1 + 80
Step 2: Since the reminder 138 ≠ 0, we apply division lemma to 80 and 138, to get
138 = 80 x 1 + 58
Step 3: We consider the new divisor 80 and the new remainder 58, and apply the division lemma to get
80 = 58 x 1 + 22
We consider the new divisor 58 and the new remainder 22,and apply the division lemma to get
58 = 22 x 2 + 14
We consider the new divisor 22 and the new remainder 14,and apply the division lemma to get
22 = 14 x 1 + 8
We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get
14 = 8 x 1 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 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 218 and 138 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(22,14) = HCF(58,22) = HCF(80,58) = HCF(138,80) = HCF(218,138) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 61 > 2, we apply the division lemma to 61 and 2, to get
61 = 2 x 30 + 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 61 is 1
Notice that 1 = HCF(2,1) = HCF(61,2) .
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Frequently Asked Questions on HCF of 218, 138, 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 218, 138, 61?
Answer: HCF of 218, 138, 61 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 218, 138, 61 using Euclid's Algorithm?
Answer: For arbitrary numbers 218, 138, 61 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.