Highest Common Factor of 121, 205, 182 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 121, 205, 182 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 121, 205, 182 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 121, 205, 182 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 121, 205, 182 is 1.
HCF(121, 205, 182) = 1
HCF of 121, 205, 182 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 121, 205, 182 is 1.
Highest Common Factor of 121,205,182 is 1
Step 1: Since 205 > 121, we apply the division lemma to 205 and 121, to get
205 = 121 x 1 + 84
Step 2: Since the reminder 121 ≠ 0, we apply division lemma to 84 and 121, to get
121 = 84 x 1 + 37
Step 3: We consider the new divisor 84 and the new remainder 37, and apply the division lemma to get
84 = 37 x 2 + 10
We consider the new divisor 37 and the new remainder 10,and apply the division lemma to get
37 = 10 x 3 + 7
We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get
10 = 7 x 1 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 121 and 205 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(37,10) = HCF(84,37) = HCF(121,84) = HCF(205,121) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 182 > 1, we apply the division lemma to 182 and 1, to get
182 = 1 x 182 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 182 is 1
Notice that 1 = HCF(182,1) .
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Frequently Asked Questions on HCF of 121, 205, 182 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 121, 205, 182?
Answer: HCF of 121, 205, 182 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 121, 205, 182 using Euclid's Algorithm?
Answer: For arbitrary numbers 121, 205, 182 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.