Highest Common Factor of 500, 580, 32 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 500, 580, 32 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 500, 580, 32 is 4 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 500, 580, 32 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 500, 580, 32 is 4.
HCF(500, 580, 32) = 4
HCF of 500, 580, 32 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 500, 580, 32 is 4.
Highest Common Factor of 500,580,32 is 4
Step 1: Since 580 > 500, we apply the division lemma to 580 and 500, to get
580 = 500 x 1 + 80
Step 2: Since the reminder 500 ≠ 0, we apply division lemma to 80 and 500, to get
500 = 80 x 6 + 20
Step 3: We consider the new divisor 80 and the new remainder 20, and apply the division lemma to get
80 = 20 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 500 and 580 is 20
Notice that 20 = HCF(80,20) = HCF(500,80) = HCF(580,500) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 32 > 20, we apply the division lemma to 32 and 20, to get
32 = 20 x 1 + 12
Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 12 and 20, to get
20 = 12 x 1 + 8
Step 3: We consider the new divisor 12 and the new remainder 8, and apply the division lemma to get
12 = 8 x 1 + 4
We consider the new divisor 8 and the new remainder 4, and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 20 and 32 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(20,12) = HCF(32,20) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 500, 580, 32 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 500, 580, 32?
Answer: HCF of 500, 580, 32 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 500, 580, 32 using Euclid's Algorithm?
Answer: For arbitrary numbers 500, 580, 32 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.