Highest Common Factor of 405, 237, 419 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 405, 237, 419 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 405, 237, 419 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 405, 237, 419 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 405, 237, 419 is 1.
HCF(405, 237, 419) = 1
HCF of 405, 237, 419 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 405, 237, 419 is 1.
Highest Common Factor of 405,237,419 is 1
Step 1: Since 405 > 237, we apply the division lemma to 405 and 237, to get
405 = 237 x 1 + 168
Step 2: Since the reminder 237 ≠ 0, we apply division lemma to 168 and 237, to get
237 = 168 x 1 + 69
Step 3: We consider the new divisor 168 and the new remainder 69, and apply the division lemma to get
168 = 69 x 2 + 30
We consider the new divisor 69 and the new remainder 30,and apply the division lemma to get
69 = 30 x 2 + 9
We consider the new divisor 30 and the new remainder 9,and apply the division lemma to get
30 = 9 x 3 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 405 and 237 is 3
Notice that 3 = HCF(9,3) = HCF(30,9) = HCF(69,30) = HCF(168,69) = HCF(237,168) = HCF(405,237) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 419 > 3, we apply the division lemma to 419 and 3, to get
419 = 3 x 139 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: 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 3 and 419 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(419,3) .
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Frequently Asked Questions on HCF of 405, 237, 419 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 405, 237, 419?
Answer: HCF of 405, 237, 419 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 405, 237, 419 using Euclid's Algorithm?
Answer: For arbitrary numbers 405, 237, 419 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.