Highest Common Factor of 9971, 3415 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 9971, 3415 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 9971, 3415 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 9971, 3415 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 9971, 3415 is 1.
HCF(9971, 3415) = 1
HCF of 9971, 3415 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9971, 3415 is 1.
Highest Common Factor of 9971,3415 is 1
Step 1: Since 9971 > 3415, we apply the division lemma to 9971 and 3415, to get
9971 = 3415 x 2 + 3141
Step 2: Since the reminder 3415 ≠ 0, we apply division lemma to 3141 and 3415, to get
3415 = 3141 x 1 + 274
Step 3: We consider the new divisor 3141 and the new remainder 274, and apply the division lemma to get
3141 = 274 x 11 + 127
We consider the new divisor 274 and the new remainder 127,and apply the division lemma to get
274 = 127 x 2 + 20
We consider the new divisor 127 and the new remainder 20,and apply the division lemma to get
127 = 20 x 6 + 7
We consider the new divisor 20 and the new remainder 7,and apply the division lemma to get
20 = 7 x 2 + 6
We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get
7 = 6 x 1 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 9971 and 3415 is 1
Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(20,7) = HCF(127,20) = HCF(274,127) = HCF(3141,274) = HCF(3415,3141) = HCF(9971,3415) .
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Frequently Asked Questions on HCF of 9971, 3415 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 9971, 3415?
Answer: HCF of 9971, 3415 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9971, 3415 using Euclid's Algorithm?
Answer: For arbitrary numbers 9971, 3415 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.