Highest Common Factor of 8144, 2412 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 8144, 2412 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 8144, 2412 is 4 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 8144, 2412 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 8144, 2412 is 4.
HCF(8144, 2412) = 4
HCF of 8144, 2412 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8144, 2412 is 4.
Highest Common Factor of 8144,2412 is 4
Step 1: Since 8144 > 2412, we apply the division lemma to 8144 and 2412, to get
8144 = 2412 x 3 + 908
Step 2: Since the reminder 2412 ≠ 0, we apply division lemma to 908 and 2412, to get
2412 = 908 x 2 + 596
Step 3: We consider the new divisor 908 and the new remainder 596, and apply the division lemma to get
908 = 596 x 1 + 312
We consider the new divisor 596 and the new remainder 312,and apply the division lemma to get
596 = 312 x 1 + 284
We consider the new divisor 312 and the new remainder 284,and apply the division lemma to get
312 = 284 x 1 + 28
We consider the new divisor 284 and the new remainder 28,and apply the division lemma to get
284 = 28 x 10 + 4
We consider the new divisor 28 and the new remainder 4,and apply the division lemma to get
28 = 4 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 8144 and 2412 is 4
Notice that 4 = HCF(28,4) = HCF(284,28) = HCF(312,284) = HCF(596,312) = HCF(908,596) = HCF(2412,908) = HCF(8144,2412) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 8144, 2412 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 8144, 2412?
Answer: HCF of 8144, 2412 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8144, 2412 using Euclid's Algorithm?
Answer: For arbitrary numbers 8144, 2412 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
