Highest Common Factor of 2015, 2178 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 2015, 2178 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2015, 2178 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 2015, 2178 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 2015, 2178 is 1.
HCF(2015, 2178) = 1
HCF of 2015, 2178 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2015, 2178 is 1.
Highest Common Factor of 2015,2178 is 1
Step 1: Since 2178 > 2015, we apply the division lemma to 2178 and 2015, to get
2178 = 2015 x 1 + 163
Step 2: Since the reminder 2015 ≠ 0, we apply division lemma to 163 and 2015, to get
2015 = 163 x 12 + 59
Step 3: We consider the new divisor 163 and the new remainder 59, and apply the division lemma to get
163 = 59 x 2 + 45
We consider the new divisor 59 and the new remainder 45,and apply the division lemma to get
59 = 45 x 1 + 14
We consider the new divisor 45 and the new remainder 14,and apply the division lemma to get
45 = 14 x 3 + 3
We consider the new divisor 14 and the new remainder 3,and apply the division lemma to get
14 = 3 x 4 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 2015 and 2178 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(45,14) = HCF(59,45) = HCF(163,59) = HCF(2015,163) = HCF(2178,2015) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 2015, 2178 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 2015, 2178?
Answer: HCF of 2015, 2178 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2015, 2178 using Euclid's Algorithm?
Answer: For arbitrary numbers 2015, 2178 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.