Highest Common Factor of 909, 712, 558 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 909, 712, 558 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 909, 712, 558 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 909, 712, 558 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 909, 712, 558 is 1.

HCF(909, 712, 558) = 1

HCF of 909, 712, 558 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 909, 712, 558 is 1.

Highest Common Factor of 909,712,558 using Euclid's algorithm

Highest Common Factor of 909,712,558 is 1

Step 1: Since 909 > 712, we apply the division lemma to 909 and 712, to get

909 = 712 x 1 + 197

Step 2: Since the reminder 712 ≠ 0, we apply division lemma to 197 and 712, to get

712 = 197 x 3 + 121

Step 3: We consider the new divisor 197 and the new remainder 121, and apply the division lemma to get

197 = 121 x 1 + 76

We consider the new divisor 121 and the new remainder 76,and apply the division lemma to get

121 = 76 x 1 + 45

We consider the new divisor 76 and the new remainder 45,and apply the division lemma to get

76 = 45 x 1 + 31

We consider the new divisor 45 and the new remainder 31,and apply the division lemma to get

45 = 31 x 1 + 14

We consider the new divisor 31 and the new remainder 14,and apply the division lemma to get

31 = 14 x 2 + 3

We consider the new divisor 14 and the new remainder 3,and apply the division lemma to get

14 = 3 x 4 + 2

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 909 and 712 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(31,14) = HCF(45,31) = HCF(76,45) = HCF(121,76) = HCF(197,121) = HCF(712,197) = HCF(909,712) .

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

Step 1: Since 558 > 1, we apply the division lemma to 558 and 1, to get

558 = 1 x 558 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 558 is 1

Notice that 1 = HCF(558,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 909, 712, 558 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 909, 712, 558?

Answer: HCF of 909, 712, 558 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 909, 712, 558 using Euclid's Algorithm?

Answer: For arbitrary numbers 909, 712, 558 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.