Highest Common Factor of 997, 21301 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, 21301 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 997, 21301 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, 21301 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, 21301 is 1.
HCF(997, 21301) = 1
HCF of 997, 21301 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, 21301 is 1.
Highest Common Factor of 997,21301 is 1
Step 1: Since 21301 > 997, we apply the division lemma to 21301 and 997, to get
21301 = 997 x 21 + 364
Step 2: Since the reminder 997 ≠ 0, we apply division lemma to 364 and 997, to get
997 = 364 x 2 + 269
Step 3: We consider the new divisor 364 and the new remainder 269, and apply the division lemma to get
364 = 269 x 1 + 95
We consider the new divisor 269 and the new remainder 95,and apply the division lemma to get
269 = 95 x 2 + 79
We consider the new divisor 95 and the new remainder 79,and apply the division lemma to get
95 = 79 x 1 + 16
We consider the new divisor 79 and the new remainder 16,and apply the division lemma to get
79 = 16 x 4 + 15
We consider the new divisor 16 and the new remainder 15,and apply the division lemma to get
16 = 15 x 1 + 1
We consider the new divisor 15 and the new remainder 1,and apply the division lemma to get
15 = 1 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 997 and 21301 is 1
Notice that 1 = HCF(15,1) = HCF(16,15) = HCF(79,16) = HCF(95,79) = HCF(269,95) = HCF(364,269) = HCF(997,364) = HCF(21301,997) .
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Frequently Asked Questions on HCF of 997, 21301 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, 21301?
Answer: HCF of 997, 21301 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 997, 21301 using Euclid's Algorithm?
Answer: For arbitrary numbers 997, 21301 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.