Highest Common Factor of 574, 450 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 574, 450 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 574, 450 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 574, 450 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 574, 450 is 2.
HCF(574, 450) = 2
HCF of 574, 450 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 574, 450 is 2.
Highest Common Factor of 574,450 is 2
Step 1: Since 574 > 450, we apply the division lemma to 574 and 450, to get
574 = 450 x 1 + 124
Step 2: Since the reminder 450 ≠ 0, we apply division lemma to 124 and 450, to get
450 = 124 x 3 + 78
Step 3: We consider the new divisor 124 and the new remainder 78, and apply the division lemma to get
124 = 78 x 1 + 46
We consider the new divisor 78 and the new remainder 46,and apply the division lemma to get
78 = 46 x 1 + 32
We consider the new divisor 46 and the new remainder 32,and apply the division lemma to get
46 = 32 x 1 + 14
We consider the new divisor 32 and the new remainder 14,and apply the division lemma to get
32 = 14 x 2 + 4
We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get
14 = 4 x 3 + 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 574 and 450 is 2
Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(32,14) = HCF(46,32) = HCF(78,46) = HCF(124,78) = HCF(450,124) = HCF(574,450) .
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Frequently Asked Questions on HCF of 574, 450 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 574, 450?
Answer: HCF of 574, 450 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 574, 450 using Euclid's Algorithm?
Answer: For arbitrary numbers 574, 450 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.