Highest Common Factor of 2304, 6874 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 2304, 6874 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 2304, 6874 is 2 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 2304, 6874 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 2304, 6874 is 2.
HCF(2304, 6874) = 2
HCF of 2304, 6874 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2304, 6874 is 2.
Highest Common Factor of 2304,6874 is 2
Step 1: Since 6874 > 2304, we apply the division lemma to 6874 and 2304, to get
6874 = 2304 x 2 + 2266
Step 2: Since the reminder 2304 ≠ 0, we apply division lemma to 2266 and 2304, to get
2304 = 2266 x 1 + 38
Step 3: We consider the new divisor 2266 and the new remainder 38, and apply the division lemma to get
2266 = 38 x 59 + 24
We consider the new divisor 38 and the new remainder 24,and apply the division lemma to get
38 = 24 x 1 + 14
We consider the new divisor 24 and the new remainder 14,and apply the division lemma to get
24 = 14 x 1 + 10
We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get
14 = 10 x 1 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2304 and 6874 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(24,14) = HCF(38,24) = HCF(2266,38) = HCF(2304,2266) = HCF(6874,2304) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 2304, 6874 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 2304, 6874?
Answer: HCF of 2304, 6874 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2304, 6874 using Euclid's Algorithm?
Answer: For arbitrary numbers 2304, 6874 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.