Highest Common Factor of 574, 490, 31 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, 490, 31 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 574, 490, 31 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 574, 490, 31 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, 490, 31 is 1.
HCF(574, 490, 31) = 1
HCF of 574, 490, 31 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, 490, 31 is 1.
Highest Common Factor of 574,490,31 is 1
Step 1: Since 574 > 490, we apply the division lemma to 574 and 490, to get
574 = 490 x 1 + 84
Step 2: Since the reminder 490 ≠ 0, we apply division lemma to 84 and 490, to get
490 = 84 x 5 + 70
Step 3: We consider the new divisor 84 and the new remainder 70, and apply the division lemma to get
84 = 70 x 1 + 14
We consider the new divisor 70 and the new remainder 14, and apply the division lemma to get
70 = 14 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 574 and 490 is 14
Notice that 14 = HCF(70,14) = HCF(84,70) = HCF(490,84) = HCF(574,490) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 31 > 14, we apply the division lemma to 31 and 14, to get
31 = 14 x 2 + 3
Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 3 and 14, to get
14 = 3 x 4 + 2
Step 3: 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 14 and 31 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(31,14) .
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Frequently Asked Questions on HCF of 574, 490, 31 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, 490, 31?
Answer: HCF of 574, 490, 31 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 574, 490, 31 using Euclid's Algorithm?
Answer: For arbitrary numbers 574, 490, 31 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.