Highest Common Factor of 775, 215, 598 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 775, 215, 598 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 775, 215, 598 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 775, 215, 598 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 775, 215, 598 is 1.

HCF(775, 215, 598) = 1

HCF of 775, 215, 598 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 775, 215, 598 is 1.

Highest Common Factor of 775,215,598 using Euclid's algorithm

Highest Common Factor of 775,215,598 is 1

Step 1: Since 775 > 215, we apply the division lemma to 775 and 215, to get

775 = 215 x 3 + 130

Step 2: Since the reminder 215 ≠ 0, we apply division lemma to 130 and 215, to get

215 = 130 x 1 + 85

Step 3: We consider the new divisor 130 and the new remainder 85, and apply the division lemma to get

130 = 85 x 1 + 45

We consider the new divisor 85 and the new remainder 45,and apply the division lemma to get

85 = 45 x 1 + 40

We consider the new divisor 45 and the new remainder 40,and apply the division lemma to get

45 = 40 x 1 + 5

We consider the new divisor 40 and the new remainder 5,and apply the division lemma to get

40 = 5 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 775 and 215 is 5

Notice that 5 = HCF(40,5) = HCF(45,40) = HCF(85,45) = HCF(130,85) = HCF(215,130) = HCF(775,215) .

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

Step 1: Since 598 > 5, we apply the division lemma to 598 and 5, to get

598 = 5 x 119 + 3

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get

5 = 3 x 1 + 2

Step 3: We consider the new divisor 3 and the new remainder 2, and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 5 and 598 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(598,5) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 775, 215, 598 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 775, 215, 598?

Answer: HCF of 775, 215, 598 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 775, 215, 598 using Euclid's Algorithm?

Answer: For arbitrary numbers 775, 215, 598 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.