Highest Common Factor of 135, 258, 344 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 135, 258, 344 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 135, 258, 344 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 135, 258, 344 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 135, 258, 344 is 1.
HCF(135, 258, 344) = 1
HCF of 135, 258, 344 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 135, 258, 344 is 1.
Highest Common Factor of 135,258,344 is 1
Step 1: Since 258 > 135, we apply the division lemma to 258 and 135, to get
258 = 135 x 1 + 123
Step 2: Since the reminder 135 ≠ 0, we apply division lemma to 123 and 135, to get
135 = 123 x 1 + 12
Step 3: We consider the new divisor 123 and the new remainder 12, and apply the division lemma to get
123 = 12 x 10 + 3
We consider the new divisor 12 and the new remainder 3, and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 135 and 258 is 3
Notice that 3 = HCF(12,3) = HCF(123,12) = HCF(135,123) = HCF(258,135) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 344 > 3, we apply the division lemma to 344 and 3, to get
344 = 3 x 114 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 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 3 and 344 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(344,3) .
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Frequently Asked Questions on HCF of 135, 258, 344 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 135, 258, 344?
Answer: HCF of 135, 258, 344 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 135, 258, 344 using Euclid's Algorithm?
Answer: For arbitrary numbers 135, 258, 344 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.