Highest Common Factor of 264, 413, 259 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 264, 413, 259 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 264, 413, 259 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 264, 413, 259 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 264, 413, 259 is 1.
HCF(264, 413, 259) = 1
HCF of 264, 413, 259 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 264, 413, 259 is 1.
Highest Common Factor of 264,413,259 is 1
Step 1: Since 413 > 264, we apply the division lemma to 413 and 264, to get
413 = 264 x 1 + 149
Step 2: Since the reminder 264 ≠ 0, we apply division lemma to 149 and 264, to get
264 = 149 x 1 + 115
Step 3: We consider the new divisor 149 and the new remainder 115, and apply the division lemma to get
149 = 115 x 1 + 34
We consider the new divisor 115 and the new remainder 34,and apply the division lemma to get
115 = 34 x 3 + 13
We consider the new divisor 34 and the new remainder 13,and apply the division lemma to get
34 = 13 x 2 + 8
We consider the new divisor 13 and the new remainder 8,and apply the division lemma to get
13 = 8 x 1 + 5
We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get
8 = 5 x 1 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
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 264 and 413 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(34,13) = HCF(115,34) = HCF(149,115) = HCF(264,149) = HCF(413,264) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 259 > 1, we apply the division lemma to 259 and 1, to get
259 = 1 x 259 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 259 is 1
Notice that 1 = HCF(259,1) .
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Frequently Asked Questions on HCF of 264, 413, 259 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 264, 413, 259?
Answer: HCF of 264, 413, 259 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 264, 413, 259 using Euclid's Algorithm?
Answer: For arbitrary numbers 264, 413, 259 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
