Highest Common Factor of 57, 35, 513 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 57, 35, 513 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 57, 35, 513 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 57, 35, 513 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 57, 35, 513 is 1.
HCF(57, 35, 513) = 1
HCF of 57, 35, 513 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 57, 35, 513 is 1.
Highest Common Factor of 57,35,513 is 1
Step 1: Since 57 > 35, we apply the division lemma to 57 and 35, to get
57 = 35 x 1 + 22
Step 2: Since the reminder 35 ≠ 0, we apply division lemma to 22 and 35, to get
35 = 22 x 1 + 13
Step 3: We consider the new divisor 22 and the new remainder 13, and apply the division lemma to get
22 = 13 x 1 + 9
We consider the new divisor 13 and the new remainder 9,and apply the division lemma to get
13 = 9 x 1 + 4
We consider the new divisor 9 and the new remainder 4,and apply the division lemma to get
9 = 4 x 2 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 57 and 35 is 1
Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(13,9) = HCF(22,13) = HCF(35,22) = HCF(57,35) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 513 > 1, we apply the division lemma to 513 and 1, to get
513 = 1 x 513 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 513 is 1
Notice that 1 = HCF(513,1) .
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Frequently Asked Questions on HCF of 57, 35, 513 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 57, 35, 513?
Answer: HCF of 57, 35, 513 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 57, 35, 513 using Euclid's Algorithm?
Answer: For arbitrary numbers 57, 35, 513 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.