Highest Common Factor of 412, 321 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 412, 321 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 412, 321 is 1 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 412, 321 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 412, 321 is 1.
HCF(412, 321) = 1
HCF of 412, 321 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 412, 321 is 1.
Highest Common Factor of 412,321 is 1
Step 1: Since 412 > 321, we apply the division lemma to 412 and 321, to get
412 = 321 x 1 + 91
Step 2: Since the reminder 321 ≠ 0, we apply division lemma to 91 and 321, to get
321 = 91 x 3 + 48
Step 3: We consider the new divisor 91 and the new remainder 48, and apply the division lemma to get
91 = 48 x 1 + 43
We consider the new divisor 48 and the new remainder 43,and apply the division lemma to get
48 = 43 x 1 + 5
We consider the new divisor 43 and the new remainder 5,and apply the division lemma to get
43 = 5 x 8 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 412 and 321 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(43,5) = HCF(48,43) = HCF(91,48) = HCF(321,91) = HCF(412,321) .
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Frequently Asked Questions on HCF of 412, 321 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 412, 321?
Answer: HCF of 412, 321 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 412, 321 using Euclid's Algorithm?
Answer: For arbitrary numbers 412, 321 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.