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Factors of 965: Prime Factorization, Methods, and Examples

965 is an odd number that has 4 factors which makes it a composite number. by definition, any number that has more than 2 factors is considered a composite number. 

the list of factors of 965 includes 1, 5, 193, and 965 where 5 and 193 are prime factors and are involved in the prime factorization of 965.

Factors of 965

Here are the factors of number 965.

Factors of 965: 1, 5, 193, and 965

Negative Factors of 965

The negative factors of 965 are similar to its positive aspects, just with a negative sign.

Negative Factors of 965: -1, -5, -193, and -965

Prime Factorization of 965

The prime factorization of 965 is the way of expressing its prime factors in the product form.

Prime Factorization: 5 x 193

In this article, we will learn about the factors of 965 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 965?

The factors of 965 are 1, 5, 193, and 965. These numbers are the factors as they do not leave any remainder when divided by 965.

The factors of 965 are classified as prime numbers and composite numbers. The prime factors of the number 965 can be determined using the prime factorization technique.

How To Find the Factors of 965?

You can find the factors of 965 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 965, create a list containing the numbers that are exactly divisible by 965 with zero remainders. One important thing to note is that 1 and 965 are the 965’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 965 are determined as follows:

\[\dfrac{965}{1} = 965\]

\[\dfrac{965}{5} = 193\]

\[\dfrac{965}{193} = 5\]

\[\dfrac{965}{965} = 1\]

Therefore, 1, 5, 193, and 965 are the factors of 965.

Total Number of Factors of 965

For 965, there are 4 positive factors and 4 negative ones. So in total, there are 8 factors of 965. 

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 965 is given as:

Factorization of 965 is 1 x 5 x 193

The exponent of 1, 5, and 193 is 1.

Adding 1 to each and multiplying them together results in 8.

Therefore, the total number of factors of 965 is 8. 4 are positive, and 4 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 965 by Prime Factorization

The number 965 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 965 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 965, 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 965 can be expressed as:

965 = 5 x 193

Factors of 965 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 965, the factor pairs can be found as:

1 x 965 = 965

5 x 193 = 965 

The possible factor pairs of 965 are given as (1, 965) and (5, 193).

All these numbers in pairs, when multiplied, give 965 as the product.

The negative factor pairs of 965 are given as:

-1 x -965 = 965 

-5 x -193 = 965

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, -5, -193, and -965 are called negative factors of 975.

The list of all the factors of 965, including positive as well as negative numbers, is given below.

Factor list of 965: 1, -1, 5, -5, 193, -193, 965, and -965

Factors of 965 Solved Examples

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

Example 1

How many factors of 965 are there?

Solution

The total number of Factors of 965 is 8.

Factors of 965 are 1, 5, 193, and 965.

Example 2

Find the factors of 965 using prime factorization.

Solution

The prime factorization of 965 is given as:

965 $\div$ 5 = 193 

193 $\div$ 193 = 1 

So the prime factorization of 965 can be written as:

5 x 193 = 965

Factors of 964|Factors List| Factors of 966

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