Highest Common Factor of 984, 7233, 2324 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 984, 7233, 2324 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 984, 7233, 2324 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 984, 7233, 2324 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 984, 7233, 2324 is 1.

HCF(984, 7233, 2324) = 1

HCF of 984, 7233, 2324 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 984, 7233, 2324 is 1.

Highest Common Factor of 984,7233,2324 using Euclid's algorithm

Highest Common Factor of 984,7233,2324 is 1

Step 1: Since 7233 > 984, we apply the division lemma to 7233 and 984, to get

7233 = 984 x 7 + 345

Step 2: Since the reminder 984 ≠ 0, we apply division lemma to 345 and 984, to get

984 = 345 x 2 + 294

Step 3: We consider the new divisor 345 and the new remainder 294, and apply the division lemma to get

345 = 294 x 1 + 51

We consider the new divisor 294 and the new remainder 51,and apply the division lemma to get

294 = 51 x 5 + 39

We consider the new divisor 51 and the new remainder 39,and apply the division lemma to get

51 = 39 x 1 + 12

We consider the new divisor 39 and the new remainder 12,and apply the division lemma to get

39 = 12 x 3 + 3

We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get

12 = 3 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 984 and 7233 is 3

Notice that 3 = HCF(12,3) = HCF(39,12) = HCF(51,39) = HCF(294,51) = HCF(345,294) = HCF(984,345) = HCF(7233,984) .

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

Step 1: Since 2324 > 3, we apply the division lemma to 2324 and 3, to get

2324 = 3 x 774 + 2

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

3 = 2 x 1 + 1

Step 3: 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 3 and 2324 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(2324,3) .

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Frequently Asked Questions on HCF of 984, 7233, 2324 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 984, 7233, 2324?

Answer: HCF of 984, 7233, 2324 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 984, 7233, 2324 using Euclid's Algorithm?

Answer: For arbitrary numbers 984, 7233, 2324 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.