Highest Common Factor of 523, 556, 301, 132 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 523, 556, 301, 132 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 523, 556, 301, 132 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 523, 556, 301, 132 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 523, 556, 301, 132 is 1.

HCF(523, 556, 301, 132) = 1

HCF of 523, 556, 301, 132 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 523, 556, 301, 132 is 1.

Highest Common Factor of 523,556,301,132 using Euclid's algorithm

Highest Common Factor of 523,556,301,132 is 1

Step 1: Since 556 > 523, we apply the division lemma to 556 and 523, to get

556 = 523 x 1 + 33

Step 2: Since the reminder 523 ≠ 0, we apply division lemma to 33 and 523, to get

523 = 33 x 15 + 28

Step 3: We consider the new divisor 33 and the new remainder 28, and apply the division lemma to get

33 = 28 x 1 + 5

We consider the new divisor 28 and the new remainder 5,and apply the division lemma to get

28 = 5 x 5 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 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 523 and 556 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(28,5) = HCF(33,28) = HCF(523,33) = HCF(556,523) .

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

Step 1: Since 301 > 1, we apply the division lemma to 301 and 1, to get

301 = 1 x 301 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 301 is 1

Notice that 1 = HCF(301,1) .

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

Step 1: Since 132 > 1, we apply the division lemma to 132 and 1, to get

132 = 1 x 132 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 132 is 1

Notice that 1 = HCF(132,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 523, 556, 301, 132 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 523, 556, 301, 132?

Answer: HCF of 523, 556, 301, 132 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 523, 556, 301, 132 using Euclid's Algorithm?

Answer: For arbitrary numbers 523, 556, 301, 132 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.