Highest Common Factor of 136, 582, 275 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 136, 582, 275 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 136, 582, 275 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 136, 582, 275 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 136, 582, 275 is 1.
HCF(136, 582, 275) = 1
HCF of 136, 582, 275 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 136, 582, 275 is 1.
Highest Common Factor of 136,582,275 is 1
Step 1: Since 582 > 136, we apply the division lemma to 582 and 136, to get
582 = 136 x 4 + 38
Step 2: Since the reminder 136 ≠ 0, we apply division lemma to 38 and 136, to get
136 = 38 x 3 + 22
Step 3: We consider the new divisor 38 and the new remainder 22, and apply the division lemma to get
38 = 22 x 1 + 16
We consider the new divisor 22 and the new remainder 16,and apply the division lemma to get
22 = 16 x 1 + 6
We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get
16 = 6 x 2 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 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 136 and 582 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(22,16) = HCF(38,22) = HCF(136,38) = HCF(582,136) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 275 > 2, we apply the division lemma to 275 and 2, to get
275 = 2 x 137 + 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 275 is 1
Notice that 1 = HCF(2,1) = HCF(275,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 136, 582, 275 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 136, 582, 275?
Answer: HCF of 136, 582, 275 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 136, 582, 275 using Euclid's Algorithm?
Answer: For arbitrary numbers 136, 582, 275 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.