Highest Common Factor of 784, 997, 528 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 784, 997, 528 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 784, 997, 528 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 784, 997, 528 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 784, 997, 528 is 1.

HCF(784, 997, 528) = 1

HCF of 784, 997, 528 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 784, 997, 528 is 1.

Highest Common Factor of 784,997,528 using Euclid's algorithm

Highest Common Factor of 784,997,528 is 1

Step 1: Since 997 > 784, we apply the division lemma to 997 and 784, to get

997 = 784 x 1 + 213

Step 2: Since the reminder 784 ≠ 0, we apply division lemma to 213 and 784, to get

784 = 213 x 3 + 145

Step 3: We consider the new divisor 213 and the new remainder 145, and apply the division lemma to get

213 = 145 x 1 + 68

We consider the new divisor 145 and the new remainder 68,and apply the division lemma to get

145 = 68 x 2 + 9

We consider the new divisor 68 and the new remainder 9,and apply the division lemma to get

68 = 9 x 7 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma 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 784 and 997 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(68,9) = HCF(145,68) = HCF(213,145) = HCF(784,213) = HCF(997,784) .

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

Step 1: Since 528 > 1, we apply the division lemma to 528 and 1, to get

528 = 1 x 528 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 528 is 1

Notice that 1 = HCF(528,1) .

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Frequently Asked Questions on HCF of 784, 997, 528 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 784, 997, 528?

Answer: HCF of 784, 997, 528 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 784, 997, 528 using Euclid's Algorithm?

Answer: For arbitrary numbers 784, 997, 528 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.