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, 760, 718 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 580, 760, 718 is 2 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, 760, 718 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, 760, 718 is 2.
HCF(580, 760, 718) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 580, 760, 718 is 2.
Step 1: Since 760 > 580, we apply the division lemma to 760 and 580, to get
760 = 580 x 1 + 180
Step 2: Since the reminder 580 ≠ 0, we apply division lemma to 180 and 580, to get
580 = 180 x 3 + 40
Step 3: We consider the new divisor 180 and the new remainder 40, and apply the division lemma to get
180 = 40 x 4 + 20
We consider the new divisor 40 and the new remainder 20, and apply the division lemma to get
40 = 20 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 580 and 760 is 20
Notice that 20 = HCF(40,20) = HCF(180,40) = HCF(580,180) = HCF(760,580) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 718 > 20, we apply the division lemma to 718 and 20, to get
718 = 20 x 35 + 18
Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 18 and 20, to get
20 = 18 x 1 + 2
Step 3: We consider the new divisor 18 and the new remainder 2, and apply the division lemma to get
18 = 2 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 20 and 718 is 2
Notice that 2 = HCF(18,2) = HCF(20,18) = HCF(718,20) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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, 760, 718?
Answer: HCF of 580, 760, 718 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 580, 760, 718 using Euclid's Algorithm?
Answer: For arbitrary numbers 580, 760, 718 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.