Highest Common Factor of 6840, 2144 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 6840, 2144 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 6840, 2144 is 8 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 6840, 2144 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 6840, 2144 is 8.
HCF(6840, 2144) = 8
HCF of 6840, 2144 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6840, 2144 is 8.
Highest Common Factor of 6840,2144 is 8
Step 1: Since 6840 > 2144, we apply the division lemma to 6840 and 2144, to get
6840 = 2144 x 3 + 408
Step 2: Since the reminder 2144 ≠ 0, we apply division lemma to 408 and 2144, to get
2144 = 408 x 5 + 104
Step 3: We consider the new divisor 408 and the new remainder 104, and apply the division lemma to get
408 = 104 x 3 + 96
We consider the new divisor 104 and the new remainder 96,and apply the division lemma to get
104 = 96 x 1 + 8
We consider the new divisor 96 and the new remainder 8,and apply the division lemma to get
96 = 8 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 6840 and 2144 is 8
Notice that 8 = HCF(96,8) = HCF(104,96) = HCF(408,104) = HCF(2144,408) = HCF(6840,2144) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 6840, 2144 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 6840, 2144?
Answer: HCF of 6840, 2144 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6840, 2144 using Euclid's Algorithm?
Answer: For arbitrary numbers 6840, 2144 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.