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 2081, 913 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2081, 913 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 2081, 913 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 2081, 913 is 1.
HCF(2081, 913) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2081, 913 is 1.
Step 1: Since 2081 > 913, we apply the division lemma to 2081 and 913, to get
2081 = 913 x 2 + 255
Step 2: Since the reminder 913 ≠ 0, we apply division lemma to 255 and 913, to get
913 = 255 x 3 + 148
Step 3: We consider the new divisor 255 and the new remainder 148, and apply the division lemma to get
255 = 148 x 1 + 107
We consider the new divisor 148 and the new remainder 107,and apply the division lemma to get
148 = 107 x 1 + 41
We consider the new divisor 107 and the new remainder 41,and apply the division lemma to get
107 = 41 x 2 + 25
We consider the new divisor 41 and the new remainder 25,and apply the division lemma to get
41 = 25 x 1 + 16
We consider the new divisor 25 and the new remainder 16,and apply the division lemma to get
25 = 16 x 1 + 9
We consider the new divisor 16 and the new remainder 9,and apply the division lemma to get
16 = 9 x 1 + 7
We consider the new divisor 9 and the new remainder 7,and apply the division lemma to get
9 = 7 x 1 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 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 2081 and 913 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(16,9) = HCF(25,16) = HCF(41,25) = HCF(107,41) = HCF(148,107) = HCF(255,148) = HCF(913,255) = HCF(2081,913) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 2081, 913?
Answer: HCF of 2081, 913 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2081, 913 using Euclid's Algorithm?
Answer: For arbitrary numbers 2081, 913 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.