Highest Common Factor of 704, 319, 592 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, 319, 592 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 704, 319, 592 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, 319, 592 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, 319, 592 is 1.

HCF(704, 319, 592) = 1

HCF of 704, 319, 592 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, 319, 592 is 1.

Highest Common Factor of 704,319,592 using Euclid's algorithm

Highest Common Factor of 704,319,592 is 1

Step 1: Since 704 > 319, we apply the division lemma to 704 and 319, to get

704 = 319 x 2 + 66

Step 2: Since the reminder 319 ≠ 0, we apply division lemma to 66 and 319, to get

319 = 66 x 4 + 55

Step 3: We consider the new divisor 66 and the new remainder 55, and apply the division lemma to get

66 = 55 x 1 + 11

We consider the new divisor 55 and the new remainder 11, and apply the division lemma to get

55 = 11 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 704 and 319 is 11

Notice that 11 = HCF(55,11) = HCF(66,55) = HCF(319,66) = HCF(704,319) .

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

Step 1: Since 592 > 11, we apply the division lemma to 592 and 11, to get

592 = 11 x 53 + 9

Step 2: Since the reminder 11 ≠ 0, we apply division lemma to 9 and 11, to get

11 = 9 x 1 + 2

Step 3: We consider the new divisor 9 and the new remainder 2, and apply the division lemma to get

9 = 2 x 4 + 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 11 and 592 is 1

Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(11,9) = HCF(592,11) .

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Frequently Asked Questions on HCF of 704, 319, 592 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, 319, 592?

Answer: HCF of 704, 319, 592 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 704, 319, 592 using Euclid's Algorithm?

Answer: For arbitrary numbers 704, 319, 592 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.