Highest Common Factor of 777, 1221, 1358 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 777, 1221, 1358 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 777, 1221, 1358 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 777, 1221, 1358 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 777, 1221, 1358 is 1.

HCF(777, 1221, 1358) = 1

HCF of 777, 1221, 1358 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 777, 1221, 1358 is 1.

Highest Common Factor of 777,1221,1358 using Euclid's algorithm

Highest Common Factor of 777,1221,1358 is 1

Step 1: Since 1221 > 777, we apply the division lemma to 1221 and 777, to get

1221 = 777 x 1 + 444

Step 2: Since the reminder 777 ≠ 0, we apply division lemma to 444 and 777, to get

777 = 444 x 1 + 333

Step 3: We consider the new divisor 444 and the new remainder 333, and apply the division lemma to get

444 = 333 x 1 + 111

We consider the new divisor 333 and the new remainder 111, and apply the division lemma to get

333 = 111 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 111, the HCF of 777 and 1221 is 111

Notice that 111 = HCF(333,111) = HCF(444,333) = HCF(777,444) = HCF(1221,777) .

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

Step 1: Since 1358 > 111, we apply the division lemma to 1358 and 111, to get

1358 = 111 x 12 + 26

Step 2: Since the reminder 111 ≠ 0, we apply division lemma to 26 and 111, to get

111 = 26 x 4 + 7

Step 3: We consider the new divisor 26 and the new remainder 7, and apply the division lemma to get

26 = 7 x 3 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 111 and 1358 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(26,7) = HCF(111,26) = HCF(1358,111) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 777, 1221, 1358 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 777, 1221, 1358?

Answer: HCF of 777, 1221, 1358 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 777, 1221, 1358 using Euclid's Algorithm?

Answer: For arbitrary numbers 777, 1221, 1358 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.