Highest Common Factor of 259, 343, 65 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 259, 343, 65 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 259, 343, 65 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 259, 343, 65 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 259, 343, 65 is 1.
HCF(259, 343, 65) = 1
HCF of 259, 343, 65 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 259, 343, 65 is 1.
Highest Common Factor of 259,343,65 is 1
Step 1: Since 343 > 259, we apply the division lemma to 343 and 259, to get
343 = 259 x 1 + 84
Step 2: Since the reminder 259 ≠ 0, we apply division lemma to 84 and 259, to get
259 = 84 x 3 + 7
Step 3: We consider the new divisor 84 and the new remainder 7, and apply the division lemma to get
84 = 7 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 259 and 343 is 7
Notice that 7 = HCF(84,7) = HCF(259,84) = HCF(343,259) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 65 > 7, we apply the division lemma to 65 and 7, to get
65 = 7 x 9 + 2
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 2 and 7, to get
7 = 2 x 3 + 1
Step 3: 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 7 and 65 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(65,7) .
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Frequently Asked Questions on HCF of 259, 343, 65 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 259, 343, 65?
Answer: HCF of 259, 343, 65 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 259, 343, 65 using Euclid's Algorithm?
Answer: For arbitrary numbers 259, 343, 65 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
