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Factors of 772: Prime Factorization, Methods, and Examples

772 is a composite number which means its number of factors is more than 2. It has a total of 6 factors and 3-factor pairs. The list of factors of 772 consists of both composite and prime numbers. The smallest composite factor is 4 and the smallest prime factor is 2. 

In this article, you will know how to find the factors of 772.

Factors of 772

Here are the factors of number 772.

Factors of 772: 1, 2, 4, 193, 386, and 772.

Negative Factors of 772

The negative factors of 772 are similar to its positive aspects, just with a negative sign.

Negative Factors of 772: – 1, -2, -4, -193, -386, and -772

Prime Factorization of 772

The prime factorization of 772 is the way of expressing its prime factors in the product form.

Prime Factorization: 2 x 2 x 193

In this article, we will learn about the factors of 772 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 772?

The factors of 772 are 1, 2, 4, 193, 386, and 772. These numbers are the factors as they do not leave any remainder when divided by 772.

The factors of 772 are classified as prime numbers and composite numbers. The prime factors of the number 772 can be determined using the prime factorization technique.

How To Find the Factors of 772?

You can find the factors of 772 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 772, create a list containing the numbers that are exactly divisible by 772 with zero remainders. One important thing to note is that 1 and 772 are the 772’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 772 are determined as follows:

\[\dfrac{772}{1} = 772\]

\[\dfrac{772}{2} = 386\]

\[\dfrac{772}{4} = 193\]

\[\dfrac{772}{193} = 4\]

\[\dfrac{772}{386} = 2\]

\[\dfrac{772}{772} = 1\]

Therefore, 1, 2, 4, 193, 386, and 772 are the factors of 772.

Total Number of Factors of 772

For 772, there are 6 positive factors and 6 negative ones. So in total, there are 12 factors of 772. 

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 772 is given as:

Factorization of 772 is 1 x 2$^2$ x 193.

The exponent of 1 and 193 is 1 whereas, the exponent of 2 is 2. 

Adding 1 to each and multiplying them together results in 12.

Therefore, the total number of factors of 772 is m. 6 are positive, and 6 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 772 by Prime Factorization

The number 772 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 772 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 772, 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 772 can be expressed as:

772 = 2$^2$ x 193

Factors of 772 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 772, the factor pairs can be found as:

1 x 772 = 772

2 x 386 = 772 

4 x 193 = 772 

The possible factor pairs of 772 are given as (1, 772), (2, 386), and (4, 193).

All these numbers in pairs, when multiplied, give 772 as the product.

The negative factor pairs of 772 are given as:

-1 x -772 = 772

-2 x -386 = 772 

-4 x -193 = 772 

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, -4, -193, -386, and -772. are called negative factors of 772.

The list of all the factors of 772, including positive as well as negative numbers, is given below.

Factor list of 772: 1, -1, 2, -2, 4, -4, 193, -193, 386, -386, 772 and -772.

Factors of 772 Solved Examples

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

Example 1

How many factors of 772 are there?

Solution

The total number of Factors of 772 is 6.

Factors of 772 are 1, 2, 4, 193, 386, and 772.

Example 2

Find the factors of 772 using prime factorization.

Solution

The prime factorization of 772 is given as:

772 $\div$ 2 = 386 

386 $\div$ 2 = 193 

193 $\div$ 193 = 1 

So the prime factorization of 386 can be written as:

2$^2$ x 193 = 772

Factors of 771|Factors List| Factors of 773

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