Highest Common Factor of 900, 557, 401 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 900, 557, 401 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 900, 557, 401 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 900, 557, 401 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 900, 557, 401 is 1.
HCF(900, 557, 401) = 1
HCF of 900, 557, 401 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 900, 557, 401 is 1.
Highest Common Factor of 900,557,401 is 1
Step 1: Since 900 > 557, we apply the division lemma to 900 and 557, to get
900 = 557 x 1 + 343
Step 2: Since the reminder 557 ≠ 0, we apply division lemma to 343 and 557, to get
557 = 343 x 1 + 214
Step 3: We consider the new divisor 343 and the new remainder 214, and apply the division lemma to get
343 = 214 x 1 + 129
We consider the new divisor 214 and the new remainder 129,and apply the division lemma to get
214 = 129 x 1 + 85
We consider the new divisor 129 and the new remainder 85,and apply the division lemma to get
129 = 85 x 1 + 44
We consider the new divisor 85 and the new remainder 44,and apply the division lemma to get
85 = 44 x 1 + 41
We consider the new divisor 44 and the new remainder 41,and apply the division lemma to get
44 = 41 x 1 + 3
We consider the new divisor 41 and the new remainder 3,and apply the division lemma to get
41 = 3 x 13 + 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 900 and 557 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(41,3) = HCF(44,41) = HCF(85,44) = HCF(129,85) = HCF(214,129) = HCF(343,214) = HCF(557,343) = HCF(900,557) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 401 > 1, we apply the division lemma to 401 and 1, to get
401 = 1 x 401 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 401 is 1
Notice that 1 = HCF(401,1) .
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Frequently Asked Questions on HCF of 900, 557, 401 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 900, 557, 401?
Answer: HCF of 900, 557, 401 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 900, 557, 401 using Euclid's Algorithm?
Answer: For arbitrary numbers 900, 557, 401 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.