Highest Common Factor of 704, 576, 921 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 704, 576, 921 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 704, 576, 921 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 704, 576, 921 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 704, 576, 921 is 1.

HCF(704, 576, 921) = 1

HCF of 704, 576, 921 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 704, 576, 921 is 1.

Highest Common Factor of 704,576,921 using Euclid's algorithm

Highest Common Factor of 704,576,921 is 1

Step 1: Since 704 > 576, we apply the division lemma to 704 and 576, to get

704 = 576 x 1 + 128

Step 2: Since the reminder 576 ≠ 0, we apply division lemma to 128 and 576, to get

576 = 128 x 4 + 64

Step 3: We consider the new divisor 128 and the new remainder 64, and apply the division lemma to get

128 = 64 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 64, the HCF of 704 and 576 is 64

Notice that 64 = HCF(128,64) = HCF(576,128) = HCF(704,576) .

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

Step 1: Since 921 > 64, we apply the division lemma to 921 and 64, to get

921 = 64 x 14 + 25

Step 2: Since the reminder 64 ≠ 0, we apply division lemma to 25 and 64, to get

64 = 25 x 2 + 14

Step 3: We consider the new divisor 25 and the new remainder 14, and apply the division lemma to get

25 = 14 x 1 + 11

We consider the new divisor 14 and the new remainder 11,and apply the division lemma to get

14 = 11 x 1 + 3

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

11 = 3 x 3 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 64 and 921 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(14,11) = HCF(25,14) = HCF(64,25) = HCF(921,64) .

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Frequently Asked Questions on HCF of 704, 576, 921 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 704, 576, 921?

Answer: HCF of 704, 576, 921 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 704, 576, 921 using Euclid's Algorithm?

Answer: For arbitrary numbers 704, 576, 921 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.