Highest Common Factor of 570, 351, 299 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 570, 351, 299 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 570, 351, 299 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 570, 351, 299 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 570, 351, 299 is 1.

HCF(570, 351, 299) = 1

HCF of 570, 351, 299 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 570, 351, 299 is 1.

Highest Common Factor of 570,351,299 using Euclid's algorithm

Highest Common Factor of 570,351,299 is 1

Step 1: Since 570 > 351, we apply the division lemma to 570 and 351, to get

570 = 351 x 1 + 219

Step 2: Since the reminder 351 ≠ 0, we apply division lemma to 219 and 351, to get

351 = 219 x 1 + 132

Step 3: We consider the new divisor 219 and the new remainder 132, and apply the division lemma to get

219 = 132 x 1 + 87

We consider the new divisor 132 and the new remainder 87,and apply the division lemma to get

132 = 87 x 1 + 45

We consider the new divisor 87 and the new remainder 45,and apply the division lemma to get

87 = 45 x 1 + 42

We consider the new divisor 45 and the new remainder 42,and apply the division lemma to get

45 = 42 x 1 + 3

We consider the new divisor 42 and the new remainder 3,and apply the division lemma to get

42 = 3 x 14 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 570 and 351 is 3

Notice that 3 = HCF(42,3) = HCF(45,42) = HCF(87,45) = HCF(132,87) = HCF(219,132) = HCF(351,219) = HCF(570,351) .

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

Step 1: Since 299 > 3, we apply the division lemma to 299 and 3, to get

299 = 3 x 99 + 2

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

3 = 2 x 1 + 1

Step 3: 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 3 and 299 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(299,3) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 570, 351, 299 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 570, 351, 299?

Answer: HCF of 570, 351, 299 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 570, 351, 299 using Euclid's Algorithm?

Answer: For arbitrary numbers 570, 351, 299 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.