Highest Common Factor of 578, 933, 782 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 578, 933, 782 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 578, 933, 782 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 578, 933, 782 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 578, 933, 782 is 1.

HCF(578, 933, 782) = 1

HCF of 578, 933, 782 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 578, 933, 782 is 1.

Highest Common Factor of 578,933,782 using Euclid's algorithm

Highest Common Factor of 578,933,782 is 1

Step 1: Since 933 > 578, we apply the division lemma to 933 and 578, to get

933 = 578 x 1 + 355

Step 2: Since the reminder 578 ≠ 0, we apply division lemma to 355 and 578, to get

578 = 355 x 1 + 223

Step 3: We consider the new divisor 355 and the new remainder 223, and apply the division lemma to get

355 = 223 x 1 + 132

We consider the new divisor 223 and the new remainder 132,and apply the division lemma to get

223 = 132 x 1 + 91

We consider the new divisor 132 and the new remainder 91,and apply the division lemma to get

132 = 91 x 1 + 41

We consider the new divisor 91 and the new remainder 41,and apply the division lemma to get

91 = 41 x 2 + 9

We consider the new divisor 41 and the new remainder 9,and apply the division lemma to get

41 = 9 x 4 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 578 and 933 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(41,9) = HCF(91,41) = HCF(132,91) = HCF(223,132) = HCF(355,223) = HCF(578,355) = HCF(933,578) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 782 > 1, we apply the division lemma to 782 and 1, to get

782 = 1 x 782 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 782 is 1

Notice that 1 = HCF(782,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 578, 933, 782 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 578, 933, 782?

Answer: HCF of 578, 933, 782 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 578, 933, 782 using Euclid's Algorithm?

Answer: For arbitrary numbers 578, 933, 782 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.