Highest Common Factor of 409, 337, 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 409, 337, 84 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 409, 337, 84 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 409, 337, 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 409, 337, 84 is 1.
HCF(409, 337, 84) = 1
HCF of 409, 337, 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 409, 337, 84 is 1.
Highest Common Factor of 409,337,84 is 1
Step 1: Since 409 > 337, we apply the division lemma to 409 and 337, to get
409 = 337 x 1 + 72
Step 2: Since the reminder 337 ≠ 0, we apply division lemma to 72 and 337, to get
337 = 72 x 4 + 49
Step 3: We consider the new divisor 72 and the new remainder 49, and apply the division lemma to get
72 = 49 x 1 + 23
We consider the new divisor 49 and the new remainder 23,and apply the division lemma to get
49 = 23 x 2 + 3
We consider the new divisor 23 and the new remainder 3,and apply the division lemma to get
23 = 3 x 7 + 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 409 and 337 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(23,3) = HCF(49,23) = HCF(72,49) = HCF(337,72) = HCF(409,337) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 84 > 1, we apply the division lemma to 84 and 1, to get
84 = 1 x 84 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 84 is 1
Notice that 1 = HCF(84,1) .
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Frequently Asked Questions on HCF of 409, 337, 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 409, 337, 84?
Answer: HCF of 409, 337, 84 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 409, 337, 84 using Euclid's Algorithm?
Answer: For arbitrary numbers 409, 337, 84 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.