Highest Common Factor of 406, 321, 338 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 406, 321, 338 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 406, 321, 338 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 406, 321, 338 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 406, 321, 338 is 1.
HCF(406, 321, 338) = 1
HCF of 406, 321, 338 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 406, 321, 338 is 1.
Highest Common Factor of 406,321,338 is 1
Step 1: Since 406 > 321, we apply the division lemma to 406 and 321, to get
406 = 321 x 1 + 85
Step 2: Since the reminder 321 ≠ 0, we apply division lemma to 85 and 321, to get
321 = 85 x 3 + 66
Step 3: We consider the new divisor 85 and the new remainder 66, and apply the division lemma to get
85 = 66 x 1 + 19
We consider the new divisor 66 and the new remainder 19,and apply the division lemma to get
66 = 19 x 3 + 9
We consider the new divisor 19 and the new remainder 9,and apply the division lemma to get
19 = 9 x 2 + 1
We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get
9 = 1 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 406 and 321 is 1
Notice that 1 = HCF(9,1) = HCF(19,9) = HCF(66,19) = HCF(85,66) = HCF(321,85) = HCF(406,321) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 338 > 1, we apply the division lemma to 338 and 1, to get
338 = 1 x 338 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 338 is 1
Notice that 1 = HCF(338,1) .
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Frequently Asked Questions on HCF of 406, 321, 338 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 406, 321, 338?
Answer: HCF of 406, 321, 338 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 406, 321, 338 using Euclid's Algorithm?
Answer: For arbitrary numbers 406, 321, 338 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.