Highest Common Factor of 704, 903, 905 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, 903, 905 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 704, 903, 905 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, 903, 905 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, 903, 905 is 1.

HCF(704, 903, 905) = 1

HCF of 704, 903, 905 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, 903, 905 is 1.

Highest Common Factor of 704,903,905 using Euclid's algorithm

Highest Common Factor of 704,903,905 is 1

Step 1: Since 903 > 704, we apply the division lemma to 903 and 704, to get

903 = 704 x 1 + 199

Step 2: Since the reminder 704 ≠ 0, we apply division lemma to 199 and 704, to get

704 = 199 x 3 + 107

Step 3: We consider the new divisor 199 and the new remainder 107, and apply the division lemma to get

199 = 107 x 1 + 92

We consider the new divisor 107 and the new remainder 92,and apply the division lemma to get

107 = 92 x 1 + 15

We consider the new divisor 92 and the new remainder 15,and apply the division lemma to get

92 = 15 x 6 + 2

We consider the new divisor 15 and the new remainder 2,and apply the division lemma to get

15 = 2 x 7 + 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 704 and 903 is 1

Notice that 1 = HCF(2,1) = HCF(15,2) = HCF(92,15) = HCF(107,92) = HCF(199,107) = HCF(704,199) = HCF(903,704) .

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

Step 1: Since 905 > 1, we apply the division lemma to 905 and 1, to get

905 = 1 x 905 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 905 is 1

Notice that 1 = HCF(905,1) .

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Frequently Asked Questions on HCF of 704, 903, 905 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, 903, 905?

Answer: HCF of 704, 903, 905 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 704, 903, 905 using Euclid's Algorithm?

Answer: For arbitrary numbers 704, 903, 905 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.