Highest Common Factor of 597, 723, 402 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 597, 723, 402 i.e. 3 the largest integer that leaves a remainder zero for all numbers.

HCF of 597, 723, 402 is 3 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 597, 723, 402 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 597, 723, 402 is 3.

HCF(597, 723, 402) = 3

HCF of 597, 723, 402 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 597, 723, 402 is 3.

Highest Common Factor of 597,723,402 using Euclid's algorithm

Highest Common Factor of 597,723,402 is 3

Step 1: Since 723 > 597, we apply the division lemma to 723 and 597, to get

723 = 597 x 1 + 126

Step 2: Since the reminder 597 ≠ 0, we apply division lemma to 126 and 597, to get

597 = 126 x 4 + 93

Step 3: We consider the new divisor 126 and the new remainder 93, and apply the division lemma to get

126 = 93 x 1 + 33

We consider the new divisor 93 and the new remainder 33,and apply the division lemma to get

93 = 33 x 2 + 27

We consider the new divisor 33 and the new remainder 27,and apply the division lemma to get

33 = 27 x 1 + 6

We consider the new divisor 27 and the new remainder 6,and apply the division lemma to get

27 = 6 x 4 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 597 and 723 is 3

Notice that 3 = HCF(6,3) = HCF(27,6) = HCF(33,27) = HCF(93,33) = HCF(126,93) = HCF(597,126) = HCF(723,597) .

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

Step 1: Since 402 > 3, we apply the division lemma to 402 and 3, to get

402 = 3 x 134 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 402 is 3

Notice that 3 = HCF(402,3) .

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Frequently Asked Questions on HCF of 597, 723, 402 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 597, 723, 402?

Answer: HCF of 597, 723, 402 is 3 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 597, 723, 402 using Euclid's Algorithm?

Answer: For arbitrary numbers 597, 723, 402 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.