Factors of 752: Prime Factorization, Methods, and Examples

The list of integers that divide 752 precisely is known as its factors; as a result, the remainder is always zero. Factors of 752 must always be whole numbers or integers; they can never be decimals of irrational numbers. 

Both numbers are factors if the product of two numbers is 752, which it is.

Factors of 752

Here are the factors of number 752.

Factors of 752: 1, 2, 4, 8, 16, 47, 94, 188, 376, and 752

Negative Factors of 752

The negative factors of 752 are similar to their positive aspects, just with a negative sign.

Negative Factors of 752: -1, -2, -4, -8, -16, -47, -94, -188, -376, and -752

Prime Factorization of 752

The prime factorization of 752 is the way of expressing its prime factors in the product form.

Prime Factorization: 2 x 2 x 2 x 2 x 47 

In this article, we will learn about the factors of 752 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 752?

The factors of 752 are 1, 2, 4, 8, 16, 47, 94, 188, 376, and 752. These numbers are the factors as they do not leave any remainder when divided by 752.

The factors of 752 are classified as prime numbers and composite numbers. The prime factors of the number 752 can be determined using the prime factorization technique.

How To Find the Factors of 752?

You can find the factors of 752 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 752, create a list containing the numbers that are exactly divisible by 752 with zero remainders. One important thing to note is that 1 and 752 are the 752’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 752 are determined as follows:

\[\dfrac{752}{1} = 752\]

\[\dfrac{752}{2} = 376\]

\[\dfrac{752}{4} = 188\]

\[\dfrac{752}{8} = 94\]

\[\dfrac{752}{16} = 47\]

\[\dfrac{752}{47} = 16\]

\[\dfrac{752}{94} = 8\]

\[\dfrac{752}{188} = 4\]

\[\dfrac{752}{376} = 2\]

\[\dfrac{752}{752} = 1\]

Therefore, 1, 2, 4, 8, 16, 47, 94, 188, 376, and 752 are the factors of 752.

Total Number of Factors of 752

For 752, there are 10 positive factors and 10 negative ones. So in total, there are 20 factors of 752. 

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 752 is given as:

Factorization of 752 is 2 x 2 x 2 x 2 x 47 .

The exponent of 2  is 4, and  47 is 1.

Adding 1 to each and multiplying them together results in 20.

Therefore, the total number of factors of 752 is 20. 10 are positive, and 10 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 752 by Prime Factorization

The number 752 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 752 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 752, 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 752 can be expressed as:

752 = 2 x 2 x 2 x 2 x 47 

Factors of 752 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 752, the factor pairs can be found as:

1 x 752 = 752

2 x 376 = 752

4 x 188 = 752

8 x 94 = 752

16 x 47 = 752

The possible factor pairs of 752 are given as (1, 752),(2, 376 ),(4, 188 ),(8, 94 ) and (16, 47 ).

All these numbers in pairs, when multiplied, give 752 as the product.

The negative factor pairs of 752 are given as:

-1 x -752 = 752

-2 x -376 = 752

-4 x -188 = 752

-8 x -94 = 752

-16 x -47 = 752

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, -8, -16, -47, -94, -188, -376, and -752 are called negative factors of 752.

The list of all the factors of 752, including positive as well as negative numbers, is given below.

Factor list of 752: 1,-1, 2,-2, 4,-4, 8,-8, 16,-16, 47,-47, 94,-94, 188,-188,376, -376,  752, and -752

Factors of752 Solved Examples.

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

Example 1

How many factors of 752 are there?

Solution

The total number of Factors of 752 is 20.

Factors of 752 are 1, 2, 4, 8, 16, 47, 94, 188, 376, and 752.

Example 2

Find the factors of 752 using prime factorization.

Solution

The prime factorization of  752 is given as:

752 $\div$ 2 =376 

376 $\div$ 2 = 188 

188 $\div$ 2 =94 

94  $\div$ 2 = 47

47 $\div$ 47 = 1

So the prime factorization of 752 can be written as:

2 x 2 x 2 x 2 x 47  = 752

Factors of 751|Factors List| Factors of 753