Highest Common Factor of 321, 378, 84 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 321, 378, 84 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 321, 378, 84 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 321, 378, 84 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 321, 378, 84 is 3.
HCF(321, 378, 84) = 3
HCF of 321, 378, 84 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 321, 378, 84 is 3.
Highest Common Factor of 321,378,84 is 3
Step 1: Since 378 > 321, we apply the division lemma to 378 and 321, to get
378 = 321 x 1 + 57
Step 2: Since the reminder 321 ≠ 0, we apply division lemma to 57 and 321, to get
321 = 57 x 5 + 36
Step 3: We consider the new divisor 57 and the new remainder 36, and apply the division lemma to get
57 = 36 x 1 + 21
We consider the new divisor 36 and the new remainder 21,and apply the division lemma to get
36 = 21 x 1 + 15
We consider the new divisor 21 and the new remainder 15,and apply the division lemma to get
21 = 15 x 1 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 321 and 378 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(21,15) = HCF(36,21) = HCF(57,36) = HCF(321,57) = HCF(378,321) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 84 > 3, we apply the division lemma to 84 and 3, to get
84 = 3 x 28 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 84 is 3
Notice that 3 = HCF(84,3) .
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Frequently Asked Questions on HCF of 321, 378, 84 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 321, 378, 84?
Answer: HCF of 321, 378, 84 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 321, 378, 84 using Euclid's Algorithm?
Answer: For arbitrary numbers 321, 378, 84 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.