Highest Common Factor of 405, 900, 571 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, 900, 571 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 405, 900, 571 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, 900, 571 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, 900, 571 is 1.
HCF(405, 900, 571) = 1
HCF of 405, 900, 571 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, 900, 571 is 1.
Highest Common Factor of 405,900,571 is 1
Step 1: Since 900 > 405, we apply the division lemma to 900 and 405, to get
900 = 405 x 2 + 90
Step 2: Since the reminder 405 ≠ 0, we apply division lemma to 90 and 405, to get
405 = 90 x 4 + 45
Step 3: We consider the new divisor 90 and the new remainder 45, and apply the division lemma to get
90 = 45 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 45, the HCF of 405 and 900 is 45
Notice that 45 = HCF(90,45) = HCF(405,90) = HCF(900,405) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 571 > 45, we apply the division lemma to 571 and 45, to get
571 = 45 x 12 + 31
Step 2: Since the reminder 45 ≠ 0, we apply division lemma to 31 and 45, to get
45 = 31 x 1 + 14
Step 3: We consider the new divisor 31 and the new remainder 14, and apply the division lemma to get
31 = 14 x 2 + 3
We consider the new divisor 14 and the new remainder 3,and apply the division lemma to get
14 = 3 x 4 + 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 45 and 571 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(31,14) = HCF(45,31) = HCF(571,45) .
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Frequently Asked Questions on HCF of 405, 900, 571 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, 900, 571?
Answer: HCF of 405, 900, 571 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 405, 900, 571 using Euclid's Algorithm?
Answer: For arbitrary numbers 405, 900, 571 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.