Highest Common Factor of 804, 712, 609 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 804, 712, 609 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 804, 712, 609 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 804, 712, 609 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 804, 712, 609 is 1.

HCF(804, 712, 609) = 1

HCF of 804, 712, 609 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 804, 712, 609 is 1.

Highest Common Factor of 804,712,609 using Euclid's algorithm

Highest Common Factor of 804,712,609 is 1

Step 1: Since 804 > 712, we apply the division lemma to 804 and 712, to get

804 = 712 x 1 + 92

Step 2: Since the reminder 712 ≠ 0, we apply division lemma to 92 and 712, to get

712 = 92 x 7 + 68

Step 3: We consider the new divisor 92 and the new remainder 68, and apply the division lemma to get

92 = 68 x 1 + 24

We consider the new divisor 68 and the new remainder 24,and apply the division lemma to get

68 = 24 x 2 + 20

We consider the new divisor 24 and the new remainder 20,and apply the division lemma to get

24 = 20 x 1 + 4

We consider the new divisor 20 and the new remainder 4,and apply the division lemma to get

20 = 4 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 804 and 712 is 4

Notice that 4 = HCF(20,4) = HCF(24,20) = HCF(68,24) = HCF(92,68) = HCF(712,92) = HCF(804,712) .

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

Step 1: Since 609 > 4, we apply the division lemma to 609 and 4, to get

609 = 4 x 152 + 1

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, 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 4 and 609 is 1

Notice that 1 = HCF(4,1) = HCF(609,4) .

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Frequently Asked Questions on HCF of 804, 712, 609 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 804, 712, 609?

Answer: HCF of 804, 712, 609 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 804, 712, 609 using Euclid's Algorithm?

Answer: For arbitrary numbers 804, 712, 609 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.