Highest Common Factor of 580, 360, 905 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 580, 360, 905 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 580, 360, 905 is 5 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 580, 360, 905 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 580, 360, 905 is 5.
HCF(580, 360, 905) = 5
HCF of 580, 360, 905 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 580, 360, 905 is 5.
Highest Common Factor of 580,360,905 is 5
Step 1: Since 580 > 360, we apply the division lemma to 580 and 360, to get
580 = 360 x 1 + 220
Step 2: Since the reminder 360 ≠ 0, we apply division lemma to 220 and 360, to get
360 = 220 x 1 + 140
Step 3: We consider the new divisor 220 and the new remainder 140, and apply the division lemma to get
220 = 140 x 1 + 80
We consider the new divisor 140 and the new remainder 80,and apply the division lemma to get
140 = 80 x 1 + 60
We consider the new divisor 80 and the new remainder 60,and apply the division lemma to get
80 = 60 x 1 + 20
We consider the new divisor 60 and the new remainder 20,and apply the division lemma to get
60 = 20 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 580 and 360 is 20
Notice that 20 = HCF(60,20) = HCF(80,60) = HCF(140,80) = HCF(220,140) = HCF(360,220) = HCF(580,360) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 905 > 20, we apply the division lemma to 905 and 20, to get
905 = 20 x 45 + 5
Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 5 and 20, to get
20 = 5 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 20 and 905 is 5
Notice that 5 = HCF(20,5) = HCF(905,20) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 580, 360, 905 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 580, 360, 905?
Answer: HCF of 580, 360, 905 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 580, 360, 905 using Euclid's Algorithm?
Answer: For arbitrary numbers 580, 360, 905 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.