Highest Common Factor of 8184, 2187 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 8184, 2187 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 8184, 2187 is 3 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 8184, 2187 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 8184, 2187 is 3.
HCF(8184, 2187) = 3
HCF of 8184, 2187 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8184, 2187 is 3.
Highest Common Factor of 8184,2187 is 3
Step 1: Since 8184 > 2187, we apply the division lemma to 8184 and 2187, to get
8184 = 2187 x 3 + 1623
Step 2: Since the reminder 2187 ≠ 0, we apply division lemma to 1623 and 2187, to get
2187 = 1623 x 1 + 564
Step 3: We consider the new divisor 1623 and the new remainder 564, and apply the division lemma to get
1623 = 564 x 2 + 495
We consider the new divisor 564 and the new remainder 495,and apply the division lemma to get
564 = 495 x 1 + 69
We consider the new divisor 495 and the new remainder 69,and apply the division lemma to get
495 = 69 x 7 + 12
We consider the new divisor 69 and the new remainder 12,and apply the division lemma to get
69 = 12 x 5 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 8184 and 2187 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(69,12) = HCF(495,69) = HCF(564,495) = HCF(1623,564) = HCF(2187,1623) = HCF(8184,2187) .
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Frequently Asked Questions on HCF of 8184, 2187 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 8184, 2187?
Answer: HCF of 8184, 2187 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8184, 2187 using Euclid's Algorithm?
Answer: For arbitrary numbers 8184, 2187 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.