Highest Common Factor of 3216, 7428, 18693 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 3216, 7428, 18693 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 3216, 7428, 18693 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 3216, 7428, 18693 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 3216, 7428, 18693 is 3.
HCF(3216, 7428, 18693) = 3
HCF of 3216, 7428, 18693 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3216, 7428, 18693 is 3.
Highest Common Factor of 3216,7428,18693 is 3
Step 1: Since 7428 > 3216, we apply the division lemma to 7428 and 3216, to get
7428 = 3216 x 2 + 996
Step 2: Since the reminder 3216 ≠ 0, we apply division lemma to 996 and 3216, to get
3216 = 996 x 3 + 228
Step 3: We consider the new divisor 996 and the new remainder 228, and apply the division lemma to get
996 = 228 x 4 + 84
We consider the new divisor 228 and the new remainder 84,and apply the division lemma to get
228 = 84 x 2 + 60
We consider the new divisor 84 and the new remainder 60,and apply the division lemma to get
84 = 60 x 1 + 24
We consider the new divisor 60 and the new remainder 24,and apply the division lemma to get
60 = 24 x 2 + 12
We consider the new divisor 24 and the new remainder 12,and apply the division lemma to get
24 = 12 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 3216 and 7428 is 12
Notice that 12 = HCF(24,12) = HCF(60,24) = HCF(84,60) = HCF(228,84) = HCF(996,228) = HCF(3216,996) = HCF(7428,3216) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 18693 > 12, we apply the division lemma to 18693 and 12, to get
18693 = 12 x 1557 + 9
Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 9 and 12, to get
12 = 9 x 1 + 3
Step 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 12 and 18693 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(18693,12) .
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Frequently Asked Questions on HCF of 3216, 7428, 18693 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 3216, 7428, 18693?
Answer: HCF of 3216, 7428, 18693 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3216, 7428, 18693 using Euclid's Algorithm?
Answer: For arbitrary numbers 3216, 7428, 18693 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.