Highest Common Factor of 672, 216, 349 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 672, 216, 349 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 672, 216, 349 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 672, 216, 349 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 672, 216, 349 is 1.

HCF(672, 216, 349) = 1

HCF of 672, 216, 349 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 672, 216, 349 is 1.

Highest Common Factor of 672,216,349 using Euclid's algorithm

Highest Common Factor of 672,216,349 is 1

Step 1: Since 672 > 216, we apply the division lemma to 672 and 216, to get

672 = 216 x 3 + 24

Step 2: Since the reminder 216 ≠ 0, we apply division lemma to 24 and 216, to get

216 = 24 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 24, the HCF of 672 and 216 is 24

Notice that 24 = HCF(216,24) = HCF(672,216) .

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

Step 1: Since 349 > 24, we apply the division lemma to 349 and 24, to get

349 = 24 x 14 + 13

Step 2: Since the reminder 24 ≠ 0, we apply division lemma to 13 and 24, to get

24 = 13 x 1 + 11

Step 3: We consider the new divisor 13 and the new remainder 11, and apply the division lemma to get

13 = 11 x 1 + 2

We consider the new divisor 11 and the new remainder 2,and apply the division lemma to get

11 = 2 x 5 + 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 24 and 349 is 1

Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(13,11) = HCF(24,13) = HCF(349,24) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 672, 216, 349 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 672, 216, 349?

Answer: HCF of 672, 216, 349 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 672, 216, 349 using Euclid's Algorithm?

Answer: For arbitrary numbers 672, 216, 349 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.