Highest Common Factor of 217, 9902 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 217, 9902 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 217, 9902 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 217, 9902 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 217, 9902 is 1.
HCF(217, 9902) = 1
HCF of 217, 9902 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 217, 9902 is 1.
Highest Common Factor of 217,9902 is 1
Step 1: Since 9902 > 217, we apply the division lemma to 9902 and 217, to get
9902 = 217 x 45 + 137
Step 2: Since the reminder 217 ≠ 0, we apply division lemma to 137 and 217, to get
217 = 137 x 1 + 80
Step 3: We consider the new divisor 137 and the new remainder 80, and apply the division lemma to get
137 = 80 x 1 + 57
We consider the new divisor 80 and the new remainder 57,and apply the division lemma to get
80 = 57 x 1 + 23
We consider the new divisor 57 and the new remainder 23,and apply the division lemma to get
57 = 23 x 2 + 11
We consider the new divisor 23 and the new remainder 11,and apply the division lemma to get
23 = 11 x 2 + 1
We consider the new divisor 11 and the new remainder 1,and apply the division lemma to get
11 = 1 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 217 and 9902 is 1
Notice that 1 = HCF(11,1) = HCF(23,11) = HCF(57,23) = HCF(80,57) = HCF(137,80) = HCF(217,137) = HCF(9902,217) .
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Frequently Asked Questions on HCF of 217, 9902 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 217, 9902?
Answer: HCF of 217, 9902 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 217, 9902 using Euclid's Algorithm?
Answer: For arbitrary numbers 217, 9902 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.