Highest Common Factor of 1613, 2071 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 1613, 2071 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 1613, 2071 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 1613, 2071 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 1613, 2071 is 1.
HCF(1613, 2071) = 1
HCF of 1613, 2071 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1613, 2071 is 1.
Highest Common Factor of 1613,2071 is 1
Step 1: Since 2071 > 1613, we apply the division lemma to 2071 and 1613, to get
2071 = 1613 x 1 + 458
Step 2: Since the reminder 1613 ≠ 0, we apply division lemma to 458 and 1613, to get
1613 = 458 x 3 + 239
Step 3: We consider the new divisor 458 and the new remainder 239, and apply the division lemma to get
458 = 239 x 1 + 219
We consider the new divisor 239 and the new remainder 219,and apply the division lemma to get
239 = 219 x 1 + 20
We consider the new divisor 219 and the new remainder 20,and apply the division lemma to get
219 = 20 x 10 + 19
We consider the new divisor 20 and the new remainder 19,and apply the division lemma to get
20 = 19 x 1 + 1
We consider the new divisor 19 and the new remainder 1,and apply the division lemma to get
19 = 1 x 19 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1613 and 2071 is 1
Notice that 1 = HCF(19,1) = HCF(20,19) = HCF(219,20) = HCF(239,219) = HCF(458,239) = HCF(1613,458) = HCF(2071,1613) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 1613, 2071 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 1613, 2071?
Answer: HCF of 1613, 2071 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1613, 2071 using Euclid's Algorithm?
Answer: For arbitrary numbers 1613, 2071 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
