Highest Common Factor of 3630, 4184, 27214 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 3630, 4184, 27214 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 3630, 4184, 27214 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 3630, 4184, 27214 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 3630, 4184, 27214 is 2.
HCF(3630, 4184, 27214) = 2
HCF of 3630, 4184, 27214 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3630, 4184, 27214 is 2.
Highest Common Factor of 3630,4184,27214 is 2
Step 1: Since 4184 > 3630, we apply the division lemma to 4184 and 3630, to get
4184 = 3630 x 1 + 554
Step 2: Since the reminder 3630 ≠ 0, we apply division lemma to 554 and 3630, to get
3630 = 554 x 6 + 306
Step 3: We consider the new divisor 554 and the new remainder 306, and apply the division lemma to get
554 = 306 x 1 + 248
We consider the new divisor 306 and the new remainder 248,and apply the division lemma to get
306 = 248 x 1 + 58
We consider the new divisor 248 and the new remainder 58,and apply the division lemma to get
248 = 58 x 4 + 16
We consider the new divisor 58 and the new remainder 16,and apply the division lemma to get
58 = 16 x 3 + 10
We consider the new divisor 16 and the new remainder 10,and apply the division lemma to get
16 = 10 x 1 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 3630 and 4184 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(58,16) = HCF(248,58) = HCF(306,248) = HCF(554,306) = HCF(3630,554) = HCF(4184,3630) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 27214 > 2, we apply the division lemma to 27214 and 2, to get
27214 = 2 x 13607 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 27214 is 2
Notice that 2 = HCF(27214,2) .
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Frequently Asked Questions on HCF of 3630, 4184, 27214 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 3630, 4184, 27214?
Answer: HCF of 3630, 4184, 27214 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3630, 4184, 27214 using Euclid's Algorithm?
Answer: For arbitrary numbers 3630, 4184, 27214 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
