Highest Common Factor of 114, 214, 97 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 114, 214, 97 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 114, 214, 97 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 114, 214, 97 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 114, 214, 97 is 1.
HCF(114, 214, 97) = 1
HCF of 114, 214, 97 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 114, 214, 97 is 1.
Highest Common Factor of 114,214,97 is 1
Step 1: Since 214 > 114, we apply the division lemma to 214 and 114, to get
214 = 114 x 1 + 100
Step 2: Since the reminder 114 ≠ 0, we apply division lemma to 100 and 114, to get
114 = 100 x 1 + 14
Step 3: We consider the new divisor 100 and the new remainder 14, and apply the division lemma to get
100 = 14 x 7 + 2
We consider the new divisor 14 and the new remainder 2, and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 114 and 214 is 2
Notice that 2 = HCF(14,2) = HCF(100,14) = HCF(114,100) = HCF(214,114) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 97 > 2, we apply the division lemma to 97 and 2, to get
97 = 2 x 48 + 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 97 is 1
Notice that 1 = HCF(2,1) = HCF(97,2) .
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Frequently Asked Questions on HCF of 114, 214, 97 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 114, 214, 97?
Answer: HCF of 114, 214, 97 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 114, 214, 97 using Euclid's Algorithm?
Answer: For arbitrary numbers 114, 214, 97 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.