Highest Common Factor of 345, 546, 409 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 345, 546, 409 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 345, 546, 409 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 345, 546, 409 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 345, 546, 409 is 1.
HCF(345, 546, 409) = 1
HCF of 345, 546, 409 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 345, 546, 409 is 1.
Highest Common Factor of 345,546,409 is 1
Step 1: Since 546 > 345, we apply the division lemma to 546 and 345, to get
546 = 345 x 1 + 201
Step 2: Since the reminder 345 ≠ 0, we apply division lemma to 201 and 345, to get
345 = 201 x 1 + 144
Step 3: We consider the new divisor 201 and the new remainder 144, and apply the division lemma to get
201 = 144 x 1 + 57
We consider the new divisor 144 and the new remainder 57,and apply the division lemma to get
144 = 57 x 2 + 30
We consider the new divisor 57 and the new remainder 30,and apply the division lemma to get
57 = 30 x 1 + 27
We consider the new divisor 30 and the new remainder 27,and apply the division lemma to get
30 = 27 x 1 + 3
We consider the new divisor 27 and the new remainder 3,and apply the division lemma to get
27 = 3 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 345 and 546 is 3
Notice that 3 = HCF(27,3) = HCF(30,27) = HCF(57,30) = HCF(144,57) = HCF(201,144) = HCF(345,201) = HCF(546,345) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 409 > 3, we apply the division lemma to 409 and 3, to get
409 = 3 x 136 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 409 is 1
Notice that 1 = HCF(3,1) = HCF(409,3) .
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Frequently Asked Questions on HCF of 345, 546, 409 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 345, 546, 409?
Answer: HCF of 345, 546, 409 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 345, 546, 409 using Euclid's Algorithm?
Answer: For arbitrary numbers 345, 546, 409 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.