Highest Common Factor of 428, 574, 800 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 428, 574, 800 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 428, 574, 800 is 2 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 428, 574, 800 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 428, 574, 800 is 2.
HCF(428, 574, 800) = 2
HCF of 428, 574, 800 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 428, 574, 800 is 2.
Highest Common Factor of 428,574,800 is 2
Step 1: Since 574 > 428, we apply the division lemma to 574 and 428, to get
574 = 428 x 1 + 146
Step 2: Since the reminder 428 ≠ 0, we apply division lemma to 146 and 428, to get
428 = 146 x 2 + 136
Step 3: We consider the new divisor 146 and the new remainder 136, and apply the division lemma to get
146 = 136 x 1 + 10
We consider the new divisor 136 and the new remainder 10,and apply the division lemma to get
136 = 10 x 13 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 428 and 574 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(136,10) = HCF(146,136) = HCF(428,146) = HCF(574,428) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 800 > 2, we apply the division lemma to 800 and 2, to get
800 = 2 x 400 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 800 is 2
Notice that 2 = HCF(800,2) .
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Frequently Asked Questions on HCF of 428, 574, 800 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 428, 574, 800?
Answer: HCF of 428, 574, 800 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 428, 574, 800 using Euclid's Algorithm?
Answer: For arbitrary numbers 428, 574, 800 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.