Highest Common Factor of 8254, 2184 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 8254, 2184 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 8254, 2184 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 8254, 2184 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 8254, 2184 is 2.
HCF(8254, 2184) = 2
HCF of 8254, 2184 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8254, 2184 is 2.
Highest Common Factor of 8254,2184 is 2
Step 1: Since 8254 > 2184, we apply the division lemma to 8254 and 2184, to get
8254 = 2184 x 3 + 1702
Step 2: Since the reminder 2184 ≠ 0, we apply division lemma to 1702 and 2184, to get
2184 = 1702 x 1 + 482
Step 3: We consider the new divisor 1702 and the new remainder 482, and apply the division lemma to get
1702 = 482 x 3 + 256
We consider the new divisor 482 and the new remainder 256,and apply the division lemma to get
482 = 256 x 1 + 226
We consider the new divisor 256 and the new remainder 226,and apply the division lemma to get
256 = 226 x 1 + 30
We consider the new divisor 226 and the new remainder 30,and apply the division lemma to get
226 = 30 x 7 + 16
We consider the new divisor 30 and the new remainder 16,and apply the division lemma to get
30 = 16 x 1 + 14
We consider the new divisor 16 and the new remainder 14,and apply the division lemma to get
16 = 14 x 1 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8254 and 2184 is 2
Notice that 2 = HCF(14,2) = HCF(16,14) = HCF(30,16) = HCF(226,30) = HCF(256,226) = HCF(482,256) = HCF(1702,482) = HCF(2184,1702) = HCF(8254,2184) .
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Frequently Asked Questions on HCF of 8254, 2184 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 8254, 2184?
Answer: HCF of 8254, 2184 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8254, 2184 using Euclid's Algorithm?
Answer: For arbitrary numbers 8254, 2184 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.