Highest Common Factor of 204, 138, 121 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 204, 138, 121 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 204, 138, 121 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 204, 138, 121 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 204, 138, 121 is 1.
HCF(204, 138, 121) = 1
HCF of 204, 138, 121 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 204, 138, 121 is 1.
Highest Common Factor of 204,138,121 is 1
Step 1: Since 204 > 138, we apply the division lemma to 204 and 138, to get
204 = 138 x 1 + 66
Step 2: Since the reminder 138 ≠ 0, we apply division lemma to 66 and 138, to get
138 = 66 x 2 + 6
Step 3: We consider the new divisor 66 and the new remainder 6, and apply the division lemma to get
66 = 6 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 204 and 138 is 6
Notice that 6 = HCF(66,6) = HCF(138,66) = HCF(204,138) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 121 > 6, we apply the division lemma to 121 and 6, to get
121 = 6 x 20 + 1
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 1 and 6, to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6 and 121 is 1
Notice that 1 = HCF(6,1) = HCF(121,6) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 204, 138, 121 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 204, 138, 121?
Answer: HCF of 204, 138, 121 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 204, 138, 121 using Euclid's Algorithm?
Answer: For arbitrary numbers 204, 138, 121 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.