Highest Common Factor of 6144, 8714 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 6144, 8714 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 6144, 8714 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 6144, 8714 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 6144, 8714 is 2.
HCF(6144, 8714) = 2
HCF of 6144, 8714 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6144, 8714 is 2.
Highest Common Factor of 6144,8714 is 2
Step 1: Since 8714 > 6144, we apply the division lemma to 8714 and 6144, to get
8714 = 6144 x 1 + 2570
Step 2: Since the reminder 6144 ≠ 0, we apply division lemma to 2570 and 6144, to get
6144 = 2570 x 2 + 1004
Step 3: We consider the new divisor 2570 and the new remainder 1004, and apply the division lemma to get
2570 = 1004 x 2 + 562
We consider the new divisor 1004 and the new remainder 562,and apply the division lemma to get
1004 = 562 x 1 + 442
We consider the new divisor 562 and the new remainder 442,and apply the division lemma to get
562 = 442 x 1 + 120
We consider the new divisor 442 and the new remainder 120,and apply the division lemma to get
442 = 120 x 3 + 82
We consider the new divisor 120 and the new remainder 82,and apply the division lemma to get
120 = 82 x 1 + 38
We consider the new divisor 82 and the new remainder 38,and apply the division lemma to get
82 = 38 x 2 + 6
We consider the new divisor 38 and the new remainder 6,and apply the division lemma to get
38 = 6 x 6 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6144 and 8714 is 2
Notice that 2 = HCF(6,2) = HCF(38,6) = HCF(82,38) = HCF(120,82) = HCF(442,120) = HCF(562,442) = HCF(1004,562) = HCF(2570,1004) = HCF(6144,2570) = HCF(8714,6144) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 6144, 8714 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 6144, 8714?
Answer: HCF of 6144, 8714 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6144, 8714 using Euclid's Algorithm?
Answer: For arbitrary numbers 6144, 8714 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.