Highest Common Factor of 413, 475, 144 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 413, 475, 144 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 413, 475, 144 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 413, 475, 144 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 413, 475, 144 is 1.
HCF(413, 475, 144) = 1
HCF of 413, 475, 144 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 413, 475, 144 is 1.
Highest Common Factor of 413,475,144 is 1
Step 1: Since 475 > 413, we apply the division lemma to 475 and 413, to get
475 = 413 x 1 + 62
Step 2: Since the reminder 413 ≠ 0, we apply division lemma to 62 and 413, to get
413 = 62 x 6 + 41
Step 3: We consider the new divisor 62 and the new remainder 41, and apply the division lemma to get
62 = 41 x 1 + 21
We consider the new divisor 41 and the new remainder 21,and apply the division lemma to get
41 = 21 x 1 + 20
We consider the new divisor 21 and the new remainder 20,and apply the division lemma to get
21 = 20 x 1 + 1
We consider the new divisor 20 and the new remainder 1,and apply the division lemma to get
20 = 1 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 413 and 475 is 1
Notice that 1 = HCF(20,1) = HCF(21,20) = HCF(41,21) = HCF(62,41) = HCF(413,62) = HCF(475,413) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 144 > 1, we apply the division lemma to 144 and 1, to get
144 = 1 x 144 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 144 is 1
Notice that 1 = HCF(144,1) .
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Frequently Asked Questions on HCF of 413, 475, 144 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 413, 475, 144?
Answer: HCF of 413, 475, 144 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 413, 475, 144 using Euclid's Algorithm?
Answer: For arbitrary numbers 413, 475, 144 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.