Highest Common Factor of 574, 448, 497 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, 448, 497 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 574, 448, 497 is 7 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, 448, 497 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, 448, 497 is 7.
HCF(574, 448, 497) = 7
HCF of 574, 448, 497 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, 448, 497 is 7.
Highest Common Factor of 574,448,497 is 7
Step 1: Since 574 > 448, we apply the division lemma to 574 and 448, to get
574 = 448 x 1 + 126
Step 2: Since the reminder 448 ≠ 0, we apply division lemma to 126 and 448, to get
448 = 126 x 3 + 70
Step 3: We consider the new divisor 126 and the new remainder 70, and apply the division lemma to get
126 = 70 x 1 + 56
We consider the new divisor 70 and the new remainder 56,and apply the division lemma to get
70 = 56 x 1 + 14
We consider the new divisor 56 and the new remainder 14,and apply the division lemma to get
56 = 14 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 574 and 448 is 14
Notice that 14 = HCF(56,14) = HCF(70,56) = HCF(126,70) = HCF(448,126) = HCF(574,448) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 497 > 14, we apply the division lemma to 497 and 14, to get
497 = 14 x 35 + 7
Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 7 and 14, to get
14 = 7 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 14 and 497 is 7
Notice that 7 = HCF(14,7) = HCF(497,14) .
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Frequently Asked Questions on HCF of 574, 448, 497 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, 448, 497?
Answer: HCF of 574, 448, 497 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 574, 448, 497 using Euclid's Algorithm?
Answer: For arbitrary numbers 574, 448, 497 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.