Highest Common Factor of 216, 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 216, 121 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 216, 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 216, 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 216, 121 is 1.
HCF(216, 121) = 1
HCF of 216, 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 216, 121 is 1.
Highest Common Factor of 216,121 is 1
Step 1: Since 216 > 121, we apply the division lemma to 216 and 121, to get
216 = 121 x 1 + 95
Step 2: Since the reminder 121 ≠ 0, we apply division lemma to 95 and 121, to get
121 = 95 x 1 + 26
Step 3: We consider the new divisor 95 and the new remainder 26, and apply the division lemma to get
95 = 26 x 3 + 17
We consider the new divisor 26 and the new remainder 17,and apply the division lemma to get
26 = 17 x 1 + 9
We consider the new divisor 17 and the new remainder 9,and apply the division lemma to get
17 = 9 x 1 + 8
We consider the new divisor 9 and the new remainder 8,and apply the division lemma to get
9 = 8 x 1 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 216 and 121 is 1
Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(17,9) = HCF(26,17) = HCF(95,26) = HCF(121,95) = HCF(216,121) .
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Frequently Asked Questions on HCF of 216, 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 216, 121?
Answer: HCF of 216, 121 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 216, 121 using Euclid's Algorithm?
Answer: For arbitrary numbers 216, 121 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.