Highest Common Factor of 923, 354, 144 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 923, 354, 144 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 923, 354, 144 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 923, 354, 144 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 923, 354, 144 is 1.

HCF(923, 354, 144) = 1

HCF of 923, 354, 144 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 923, 354, 144 is 1.

Highest Common Factor of 923,354,144 using Euclid's algorithm

Highest Common Factor of 923,354,144 is 1

Step 1: Since 923 > 354, we apply the division lemma to 923 and 354, to get

923 = 354 x 2 + 215

Step 2: Since the reminder 354 ≠ 0, we apply division lemma to 215 and 354, to get

354 = 215 x 1 + 139

Step 3: We consider the new divisor 215 and the new remainder 139, and apply the division lemma to get

215 = 139 x 1 + 76

We consider the new divisor 139 and the new remainder 76,and apply the division lemma to get

139 = 76 x 1 + 63

We consider the new divisor 76 and the new remainder 63,and apply the division lemma to get

76 = 63 x 1 + 13

We consider the new divisor 63 and the new remainder 13,and apply the division lemma to get

63 = 13 x 4 + 11

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 923 and 354 is 1

Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(13,11) = HCF(63,13) = HCF(76,63) = HCF(139,76) = HCF(215,139) = HCF(354,215) = HCF(923,354) .

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

Step 1: Since 144 > 1, we apply the division lemma to 144 and 1, to get

144 = 1 x 144 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 144 is 1

Notice that 1 = HCF(144,1) .

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Frequently Asked Questions on HCF of 923, 354, 144 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 923, 354, 144?

Answer: HCF of 923, 354, 144 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 923, 354, 144 using Euclid's Algorithm?

Answer: For arbitrary numbers 923, 354, 144 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.