Highest Common Factor of 342, 134, 459, 26 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 342, 134, 459, 26 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 342, 134, 459, 26 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 342, 134, 459, 26 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 342, 134, 459, 26 is 1.
HCF(342, 134, 459, 26) = 1
HCF of 342, 134, 459, 26 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 342, 134, 459, 26 is 1.
Highest Common Factor of 342,134,459,26 is 1
Step 1: Since 342 > 134, we apply the division lemma to 342 and 134, to get
342 = 134 x 2 + 74
Step 2: Since the reminder 134 ≠ 0, we apply division lemma to 74 and 134, to get
134 = 74 x 1 + 60
Step 3: We consider the new divisor 74 and the new remainder 60, and apply the division lemma to get
74 = 60 x 1 + 14
We consider the new divisor 60 and the new remainder 14,and apply the division lemma to get
60 = 14 x 4 + 4
We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get
14 = 4 x 3 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 342 and 134 is 2
Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(60,14) = HCF(74,60) = HCF(134,74) = HCF(342,134) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 459 > 2, we apply the division lemma to 459 and 2, to get
459 = 2 x 229 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 459 is 1
Notice that 1 = HCF(2,1) = HCF(459,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 26 > 1, we apply the division lemma to 26 and 1, to get
26 = 1 x 26 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 26 is 1
Notice that 1 = HCF(26,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 342, 134, 459, 26 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 342, 134, 459, 26?
Answer: HCF of 342, 134, 459, 26 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 342, 134, 459, 26 using Euclid's Algorithm?
Answer: For arbitrary numbers 342, 134, 459, 26 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.