Highest Common Factor of 782, 904, 768 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 782, 904, 768 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 782, 904, 768 is 2 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 782, 904, 768 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 782, 904, 768 is 2.

HCF(782, 904, 768) = 2

HCF of 782, 904, 768 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 782, 904, 768 is 2.

Highest Common Factor of 782,904,768 using Euclid's algorithm

Highest Common Factor of 782,904,768 is 2

Step 1: Since 904 > 782, we apply the division lemma to 904 and 782, to get

904 = 782 x 1 + 122

Step 2: Since the reminder 782 ≠ 0, we apply division lemma to 122 and 782, to get

782 = 122 x 6 + 50

Step 3: We consider the new divisor 122 and the new remainder 50, and apply the division lemma to get

122 = 50 x 2 + 22

We consider the new divisor 50 and the new remainder 22,and apply the division lemma to get

50 = 22 x 2 + 6

We consider the new divisor 22 and the new remainder 6,and apply the division lemma to get

22 = 6 x 3 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 782 and 904 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(22,6) = HCF(50,22) = HCF(122,50) = HCF(782,122) = HCF(904,782) .

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

Step 1: Since 768 > 2, we apply the division lemma to 768 and 2, to get

768 = 2 x 384 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 768 is 2

Notice that 2 = HCF(768,2) .

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Frequently Asked Questions on HCF of 782, 904, 768 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 782, 904, 768?

Answer: HCF of 782, 904, 768 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 782, 904, 768 using Euclid's Algorithm?

Answer: For arbitrary numbers 782, 904, 768 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.