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Factors of 774: Prime Factorization, Methods, and Examples

774 is a composite number and has 12 factors. Every composite number is a product of its composite and prime factors. when the product involves only 2 factors, the two factors make a factor pair. There is a total of 6-factor pairs of 774. 

The concept is discussed in detail below.

Factors of 774

Here are the factors of number 774.

Factors of 774: 1, 2, 3, 6, 9, 18, 43, 86, 129, 258, 387, and 774

Negative Factors of 774

The negative factors of 774 are similar to its positive aspects, just with a negative sign.

Negative Factors of 774: -1, -2, -3, -6, -9, -18, -43, -86, -129, -258, -387, and -774

Prime Factorization of 774

The prime factorization of 774 is the way of expressing its prime factors in the product form.

Prime Factorization: 2 x 3$^2$ x 43

In this article, we will learn about the factors of 774 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 774?

The factors of 774 are 1, 2, 3, 6, 9, 18, 43, 86, 129, 258, 387, and 774. These numbers are the factors as they do not leave any remainder when divided by 774.

The factors of 774 are classified as prime numbers and composite numbers. The prime factors of the number 774 can be determined using the prime factorization technique.

How To Find the Factors of 774?

You can find the factors of 774 by using the rules of divisibility. The divisibility rule states that any number, when divided by any other natural number, is said to be divisible by the number if the quotient is the whole number and the resulting remainder is zero.

To find the factors of 774, create a list containing the numbers that are exactly divisible by 774 with zero remainders. One important thing to note is that 1 and 774 are the 774’s factors as every natural number has 1 and the number itself as its factor.

1 is also called the universal factor of every number. The factors of 774 are determined as follows:

\[\dfrac{774}{1} = 774\]

\[\dfrac{774}{2} = 387\]

\[\dfrac{774}{3} = 258\]

\[\dfrac{774}{6} = 129\]

\[\dfrac{774}{9} = 86\]

\[\dfrac{774}{18} = 43\]

\[\dfrac{774}{43} = 18\]

\[\dfrac{774}{86} = 9\]

\[\dfrac{774}{129} = 6\]

\[\dfrac{774}{258} = 3\]

\[\dfrac{774}{387} = 2\]

\[\dfrac{774}{774} = 1\]

Therefore, , 2, 3, 6, 9, 18, 43, 86, 129, 258, 387, and 774. are the factors of 774.

Total Number of Factors of 774

For 774, there are 12 positive factors and 12 negative ones. So in total, there are 24 factors of 774, 

To find the total number of factors of the given number, follow the procedure mentioned below:

  1. Find the factorization/prime factorization of the given number.
  2. Demonstrate the prime factorization of the number in the form of exponent form.
  3. Add 1 to each of the exponents of the prime factor.
  4. Now, multiply the resulting exponents together. This obtained product is equivalent to the total number of factors of the given number.

By following this procedure, the total number of factors of 774 is given as:

Factorization of 774 is 1 x 2 x 3$^2$ x 43.

The exponent of 1, 2, and 43 is 1 whereas, the exponent of 3 is 2.

Adding 1 to each and multiplying them together results in 24.

Therefore, the total number of factors of 774 is 24. 12 are positive, and 12 factors are negative.

Important Notes

Here are some essential points that must be considered while finding the factors of any given number:

  • The factor of any given number must be a whole number.
  • The factors of the number cannot be in the form of decimals or fractions.
  • Factors can be positive as well as negative.
  • Negative factors are the additive inverse of the positive factors of a given number.
  • The factor of a number cannot be greater than that number.
  • Every even number has 2 as its prime factor, the smallest prime factor.

Factors of 774 by Prime Factorization

The number 774 is a composite number. Prime factorization is a valuable technique for finding the number’s prime factors and expressing the number as the product of its prime factors.

Before finding the factors of 774 using prime factorization, let us find out what prime factors are. Prime factors are the factors of any given number that are only divisible by 1 and themselves.

To start the prime factorization of 774, start dividing by its most minor prime factor. First, determine that the given number is either even or odd. If it is an even number, then 2 will be the smallest prime factor.

Continue splitting the quotient obtained until 1 is received as the quotient. The prime factorization of 774 can be expressed as:

774 = 2 x 3$^2$ x 43

Factors of 774 in Pairs

The factor pairs are the duplet of numbers that, when multiplied together, result in the factorized number. Factor pairs can be more than one depending on the total number of factors given.

For 774, the factor pairs can be found as:

1 x 774 = 774

2 x 387 = 774 

3 x 258 = 774 

6 x 129 = 774 

9 x 86 = 774 

18 x 43 = 774 

The possible factor pairs of 774 are given as (1, 774), (2, 387), (3, 258), (6, 129), (9, 86), and (18, 43).

All these numbers in pairs, when multiplied, give 774 as the product.

The negative factor pairs of 774 are given as:

-1 x -774 = 774

-2 x -387 = 774 

-3 x -258 = 774 

-6 x -129 = 774 

-9 x -86 = 774 

-18 x -43 = 774 

It is important to note that in negative factor pairs, the minus sign has been multiplied by the minus sign, due to which the resulting product is the original positive number. Therefore, -1, -2, -3, -6, -9, -18, -43, -86, -129, -258, -387, -774 are called negative factors of 774.

The list of all the factors of 774, including positive as well as negative numbers, is given below.

Factor list of 774: 1, -1, 2, -2, 3, -3, 6, -6, 9, -9 18, -18, 43, -43, 86, -86, 129, -129, 258, -258, 387,-387, 774, and -774.

Factors of 774 Solved Examples

To better understand the concept of factors, let’s solve some examples.

Example 1

How many factors of 774 are there?

Solution

The total number of Factors of 774 is 12.

Factors of 774 are , 2, 3, 6, 9, 18, 43, 86, 129, 258, 387, and  774.

Example 2

Find the factors of 774 using prime factorization.

Solution

The prime factorization of 774 is given as:

774 $\div$ 2 = 387 

387 $\div$ 3 = 129 

129 $\div$ 3 = 43 

43 $\div$ 43 = 1 

So the prime factorization of 774 can be written as:

2 x 3$^2$ x 43 = 774

Factors of 773|Factors List| Factors of 775

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