Highest Common Factor of 945, 624, 289 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 945, 624, 289 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 945, 624, 289 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 945, 624, 289 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 945, 624, 289 is 1.

HCF(945, 624, 289) = 1

HCF of 945, 624, 289 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 945, 624, 289 is 1.

Highest Common Factor of 945,624,289 using Euclid's algorithm

Highest Common Factor of 945,624,289 is 1

Step 1: Since 945 > 624, we apply the division lemma to 945 and 624, to get

945 = 624 x 1 + 321

Step 2: Since the reminder 624 ≠ 0, we apply division lemma to 321 and 624, to get

624 = 321 x 1 + 303

Step 3: We consider the new divisor 321 and the new remainder 303, and apply the division lemma to get

321 = 303 x 1 + 18

We consider the new divisor 303 and the new remainder 18,and apply the division lemma to get

303 = 18 x 16 + 15

We consider the new divisor 18 and the new remainder 15,and apply the division lemma to get

18 = 15 x 1 + 3

We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get

15 = 3 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 945 and 624 is 3

Notice that 3 = HCF(15,3) = HCF(18,15) = HCF(303,18) = HCF(321,303) = HCF(624,321) = HCF(945,624) .

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

Step 1: Since 289 > 3, we apply the division lemma to 289 and 3, to get

289 = 3 x 96 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 289 is 1

Notice that 1 = HCF(3,1) = HCF(289,3) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 945, 624, 289 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 945, 624, 289?

Answer: HCF of 945, 624, 289 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 945, 624, 289 using Euclid's Algorithm?

Answer: For arbitrary numbers 945, 624, 289 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.