Highest Common Factor of 997, 30131 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 997, 30131 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 997, 30131 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 997, 30131 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 997, 30131 is 1.
HCF(997, 30131) = 1
HCF of 997, 30131 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 997, 30131 is 1.
Highest Common Factor of 997,30131 is 1
Step 1: Since 30131 > 997, we apply the division lemma to 30131 and 997, to get
30131 = 997 x 30 + 221
Step 2: Since the reminder 997 ≠ 0, we apply division lemma to 221 and 997, to get
997 = 221 x 4 + 113
Step 3: We consider the new divisor 221 and the new remainder 113, and apply the division lemma to get
221 = 113 x 1 + 108
We consider the new divisor 113 and the new remainder 108,and apply the division lemma to get
113 = 108 x 1 + 5
We consider the new divisor 108 and the new remainder 5,and apply the division lemma to get
108 = 5 x 21 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 997 and 30131 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(108,5) = HCF(113,108) = HCF(221,113) = HCF(997,221) = HCF(30131,997) .
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Frequently Asked Questions on HCF of 997, 30131 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 997, 30131?
Answer: HCF of 997, 30131 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 997, 30131 using Euclid's Algorithm?
Answer: For arbitrary numbers 997, 30131 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.