Highest Common Factor of 8328, 3345, 73254 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 8328, 3345, 73254 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 8328, 3345, 73254 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 8328, 3345, 73254 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 8328, 3345, 73254 is 3.
HCF(8328, 3345, 73254) = 3
HCF of 8328, 3345, 73254 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8328, 3345, 73254 is 3.
Highest Common Factor of 8328,3345,73254 is 3
Step 1: Since 8328 > 3345, we apply the division lemma to 8328 and 3345, to get
8328 = 3345 x 2 + 1638
Step 2: Since the reminder 3345 ≠ 0, we apply division lemma to 1638 and 3345, to get
3345 = 1638 x 2 + 69
Step 3: We consider the new divisor 1638 and the new remainder 69, and apply the division lemma to get
1638 = 69 x 23 + 51
We consider the new divisor 69 and the new remainder 51,and apply the division lemma to get
69 = 51 x 1 + 18
We consider the new divisor 51 and the new remainder 18,and apply the division lemma to get
51 = 18 x 2 + 15
We consider the new divisor 18 and the new remainder 15,and apply the division lemma to get
18 = 15 x 1 + 3
We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 8328 and 3345 is 3
Notice that 3 = HCF(15,3) = HCF(18,15) = HCF(51,18) = HCF(69,51) = HCF(1638,69) = HCF(3345,1638) = HCF(8328,3345) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 73254 > 3, we apply the division lemma to 73254 and 3, to get
73254 = 3 x 24418 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 73254 is 3
Notice that 3 = HCF(73254,3) .
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Frequently Asked Questions on HCF of 8328, 3345, 73254 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 8328, 3345, 73254?
Answer: HCF of 8328, 3345, 73254 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8328, 3345, 73254 using Euclid's Algorithm?
Answer: For arbitrary numbers 8328, 3345, 73254 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.