Highest Common Factor of 825, 960, 778 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 825, 960, 778 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 825, 960, 778 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 825, 960, 778 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 825, 960, 778 is 1.

HCF(825, 960, 778) = 1

HCF of 825, 960, 778 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 825, 960, 778 is 1.

Highest Common Factor of 825,960,778 using Euclid's algorithm

Highest Common Factor of 825,960,778 is 1

Step 1: Since 960 > 825, we apply the division lemma to 960 and 825, to get

960 = 825 x 1 + 135

Step 2: Since the reminder 825 ≠ 0, we apply division lemma to 135 and 825, to get

825 = 135 x 6 + 15

Step 3: We consider the new divisor 135 and the new remainder 15, and apply the division lemma to get

135 = 15 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 825 and 960 is 15

Notice that 15 = HCF(135,15) = HCF(825,135) = HCF(960,825) .

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

Step 1: Since 778 > 15, we apply the division lemma to 778 and 15, to get

778 = 15 x 51 + 13

Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 13 and 15, to get

15 = 13 x 1 + 2

Step 3: We consider the new divisor 13 and the new remainder 2, and apply the division lemma to get

13 = 2 x 6 + 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 15 and 778 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(15,13) = HCF(778,15) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 825, 960, 778 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 825, 960, 778?

Answer: HCF of 825, 960, 778 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 825, 960, 778 using Euclid's Algorithm?

Answer: For arbitrary numbers 825, 960, 778 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.