Highest Common Factor of 109, 260, 13 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 109, 260, 13 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 109, 260, 13 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 109, 260, 13 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 109, 260, 13 is 1.
HCF(109, 260, 13) = 1
HCF of 109, 260, 13 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 109, 260, 13 is 1.
Highest Common Factor of 109,260,13 is 1
Step 1: Since 260 > 109, we apply the division lemma to 260 and 109, to get
260 = 109 x 2 + 42
Step 2: Since the reminder 109 ≠ 0, we apply division lemma to 42 and 109, to get
109 = 42 x 2 + 25
Step 3: We consider the new divisor 42 and the new remainder 25, and apply the division lemma to get
42 = 25 x 1 + 17
We consider the new divisor 25 and the new remainder 17,and apply the division lemma to get
25 = 17 x 1 + 8
We consider the new divisor 17 and the new remainder 8,and apply the division lemma to get
17 = 8 x 2 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 109 and 260 is 1
Notice that 1 = HCF(8,1) = HCF(17,8) = HCF(25,17) = HCF(42,25) = HCF(109,42) = HCF(260,109) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 13 > 1, we apply the division lemma to 13 and 1, to get
13 = 1 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 13 is 1
Notice that 1 = HCF(13,1) .
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Frequently Asked Questions on HCF of 109, 260, 13 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 109, 260, 13?
Answer: HCF of 109, 260, 13 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 109, 260, 13 using Euclid's Algorithm?
Answer: For arbitrary numbers 109, 260, 13 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.