Highest Common Factor of 258, 423, 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 258, 423, 513 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 258, 423, 513 is 3 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 258, 423, 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 258, 423, 513 is 3.
HCF(258, 423, 513) = 3
HCF of 258, 423, 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 258, 423, 513 is 3.
Highest Common Factor of 258,423,513 is 3
Step 1: Since 423 > 258, we apply the division lemma to 423 and 258, to get
423 = 258 x 1 + 165
Step 2: Since the reminder 258 ≠ 0, we apply division lemma to 165 and 258, to get
258 = 165 x 1 + 93
Step 3: We consider the new divisor 165 and the new remainder 93, and apply the division lemma to get
165 = 93 x 1 + 72
We consider the new divisor 93 and the new remainder 72,and apply the division lemma to get
93 = 72 x 1 + 21
We consider the new divisor 72 and the new remainder 21,and apply the division lemma to get
72 = 21 x 3 + 9
We consider the new divisor 21 and the new remainder 9,and apply the division lemma to get
21 = 9 x 2 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 258 and 423 is 3
Notice that 3 = HCF(9,3) = HCF(21,9) = HCF(72,21) = HCF(93,72) = HCF(165,93) = HCF(258,165) = HCF(423,258) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 513 > 3, we apply the division lemma to 513 and 3, to get
513 = 3 x 171 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 513 is 3
Notice that 3 = HCF(513,3) .
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Frequently Asked Questions on HCF of 258, 423, 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 258, 423, 513?
Answer: HCF of 258, 423, 513 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 258, 423, 513 using Euclid's Algorithm?
Answer: For arbitrary numbers 258, 423, 513 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.