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 2071, 5413 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2071, 5413 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 2071, 5413 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 2071, 5413 is 1.
HCF(2071, 5413) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2071, 5413 is 1.
Step 1: Since 5413 > 2071, we apply the division lemma to 5413 and 2071, to get
5413 = 2071 x 2 + 1271
Step 2: Since the reminder 2071 ≠ 0, we apply division lemma to 1271 and 2071, to get
2071 = 1271 x 1 + 800
Step 3: We consider the new divisor 1271 and the new remainder 800, and apply the division lemma to get
1271 = 800 x 1 + 471
We consider the new divisor 800 and the new remainder 471,and apply the division lemma to get
800 = 471 x 1 + 329
We consider the new divisor 471 and the new remainder 329,and apply the division lemma to get
471 = 329 x 1 + 142
We consider the new divisor 329 and the new remainder 142,and apply the division lemma to get
329 = 142 x 2 + 45
We consider the new divisor 142 and the new remainder 45,and apply the division lemma to get
142 = 45 x 3 + 7
We consider the new divisor 45 and the new remainder 7,and apply the division lemma to get
45 = 7 x 6 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2071 and 5413 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(45,7) = HCF(142,45) = HCF(329,142) = HCF(471,329) = HCF(800,471) = HCF(1271,800) = HCF(2071,1271) = HCF(5413,2071) .
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 2071, 5413?
Answer: HCF of 2071, 5413 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2071, 5413 using Euclid's Algorithm?
Answer: For arbitrary numbers 2071, 5413 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.