Highest Common Factor of 132, 697, 548 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 132, 697, 548 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 132, 697, 548 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 132, 697, 548 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 132, 697, 548 is 1.

HCF(132, 697, 548) = 1

HCF of 132, 697, 548 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 132, 697, 548 is 1.

Highest Common Factor of 132,697,548 using Euclid's algorithm

Highest Common Factor of 132,697,548 is 1

Step 1: Since 697 > 132, we apply the division lemma to 697 and 132, to get

697 = 132 x 5 + 37

Step 2: Since the reminder 132 ≠ 0, we apply division lemma to 37 and 132, to get

132 = 37 x 3 + 21

Step 3: We consider the new divisor 37 and the new remainder 21, and apply the division lemma to get

37 = 21 x 1 + 16

We consider the new divisor 21 and the new remainder 16,and apply the division lemma to get

21 = 16 x 1 + 5

We consider the new divisor 16 and the new remainder 5,and apply the division lemma to get

16 = 5 x 3 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 132 and 697 is 1

Notice that 1 = HCF(5,1) = HCF(16,5) = HCF(21,16) = HCF(37,21) = HCF(132,37) = HCF(697,132) .

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

Step 1: Since 548 > 1, we apply the division lemma to 548 and 1, to get

548 = 1 x 548 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 548 is 1

Notice that 1 = HCF(548,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 132, 697, 548 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 132, 697, 548?

Answer: HCF of 132, 697, 548 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 132, 697, 548 using Euclid's Algorithm?

Answer: For arbitrary numbers 132, 697, 548 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.