Highest Common Factor of 234, 923, 984 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 234, 923, 984 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 234, 923, 984 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 234, 923, 984 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 234, 923, 984 is 1.

HCF(234, 923, 984) = 1

HCF of 234, 923, 984 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 234, 923, 984 is 1.

Highest Common Factor of 234,923,984 using Euclid's algorithm

Highest Common Factor of 234,923,984 is 1

Step 1: Since 923 > 234, we apply the division lemma to 923 and 234, to get

923 = 234 x 3 + 221

Step 2: Since the reminder 234 ≠ 0, we apply division lemma to 221 and 234, to get

234 = 221 x 1 + 13

Step 3: We consider the new divisor 221 and the new remainder 13, and apply the division lemma to get

221 = 13 x 17 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 234 and 923 is 13

Notice that 13 = HCF(221,13) = HCF(234,221) = HCF(923,234) .

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

Step 1: Since 984 > 13, we apply the division lemma to 984 and 13, to get

984 = 13 x 75 + 9

Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 9 and 13, to get

13 = 9 x 1 + 4

Step 3: We consider the new divisor 9 and the new remainder 4, and apply the division lemma to get

9 = 4 x 2 + 1

We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 13 and 984 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(13,9) = HCF(984,13) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 234, 923, 984 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 234, 923, 984?

Answer: HCF of 234, 923, 984 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 234, 923, 984 using Euclid's Algorithm?

Answer: For arbitrary numbers 234, 923, 984 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.