Highest Common Factor of 572, 354, 504 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 572, 354, 504 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 572, 354, 504 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 572, 354, 504 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 572, 354, 504 is 2.
HCF(572, 354, 504) = 2
HCF of 572, 354, 504 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 572, 354, 504 is 2.
Highest Common Factor of 572,354,504 is 2
Step 1: Since 572 > 354, we apply the division lemma to 572 and 354, to get
572 = 354 x 1 + 218
Step 2: Since the reminder 354 ≠ 0, we apply division lemma to 218 and 354, to get
354 = 218 x 1 + 136
Step 3: We consider the new divisor 218 and the new remainder 136, and apply the division lemma to get
218 = 136 x 1 + 82
We consider the new divisor 136 and the new remainder 82,and apply the division lemma to get
136 = 82 x 1 + 54
We consider the new divisor 82 and the new remainder 54,and apply the division lemma to get
82 = 54 x 1 + 28
We consider the new divisor 54 and the new remainder 28,and apply the division lemma to get
54 = 28 x 1 + 26
We consider the new divisor 28 and the new remainder 26,and apply the division lemma to get
28 = 26 x 1 + 2
We consider the new divisor 26 and the new remainder 2,and apply the division lemma to get
26 = 2 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 572 and 354 is 2
Notice that 2 = HCF(26,2) = HCF(28,26) = HCF(54,28) = HCF(82,54) = HCF(136,82) = HCF(218,136) = HCF(354,218) = HCF(572,354) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 504 > 2, we apply the division lemma to 504 and 2, to get
504 = 2 x 252 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 504 is 2
Notice that 2 = HCF(504,2) .
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Frequently Asked Questions on HCF of 572, 354, 504 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 572, 354, 504?
Answer: HCF of 572, 354, 504 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 572, 354, 504 using Euclid's Algorithm?
Answer: For arbitrary numbers 572, 354, 504 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
