Highest Common Factor of 2986, 313 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 2986, 313 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2986, 313 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 2986, 313 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 2986, 313 is 1.
HCF(2986, 313) = 1
HCF of 2986, 313 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2986, 313 is 1.
Highest Common Factor of 2986,313 is 1
Step 1: Since 2986 > 313, we apply the division lemma to 2986 and 313, to get
2986 = 313 x 9 + 169
Step 2: Since the reminder 313 ≠ 0, we apply division lemma to 169 and 313, to get
313 = 169 x 1 + 144
Step 3: We consider the new divisor 169 and the new remainder 144, and apply the division lemma to get
169 = 144 x 1 + 25
We consider the new divisor 144 and the new remainder 25,and apply the division lemma to get
144 = 25 x 5 + 19
We consider the new divisor 25 and the new remainder 19,and apply the division lemma to get
25 = 19 x 1 + 6
We consider the new divisor 19 and the new remainder 6,and apply the division lemma to get
19 = 6 x 3 + 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 2986 and 313 is 1
Notice that 1 = HCF(6,1) = HCF(19,6) = HCF(25,19) = HCF(144,25) = HCF(169,144) = HCF(313,169) = HCF(2986,313) .
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Frequently Asked Questions on HCF of 2986, 313 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 2986, 313?
Answer: HCF of 2986, 313 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2986, 313 using Euclid's Algorithm?
Answer: For arbitrary numbers 2986, 313 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.