Factors of 104

The factors of a number can either be prime or composite. Hence, 104 is an even composite number itself which constitutes of factors which are either prime or composite. Let's learn to calculate the factors of 104, prime factors of 104, and factors of 104 in pairs along with solved examples for a better understanding.

• Factors of 104: 1, 2, 4, 8, 13, 26, 52 and 104
• Prime Factorization of 104: 104 = 2³ × 13

What are the Factors of 104?

Factors of 104 are the numbers which when multiplied in pairs give the product as 104. These factors can be negative as well. The factor of a number is that number which divides it completely, i.e., leaves no remainder.For example: To find the factors of the number 104, we will have to perform division on 104 and find the numbers which divide 104 completely, leaving no remainders.

The diagram below provides the representation of the above definition:

How to Calculate the Factors of 104?

To calculate the factors of any number, say, 104, we need to find all the numbers that would divide 104 without leaving any remainder. We start with the number 1, then check for numbers 2, 3, 4, 5, 6, 7, etc. up to 52 (half of 104).  The number 1 and the number itself are always factors of the given number.

Refer to the following table to check division 104 by its factors:

Hence, the factors of 104 are 1, 2, 4, 8, 13, 26, 52 and 104.

Explore factors using illustrations and interactive examples

• Factors of 105 - The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105
• Factors of 140 - The factors of 104 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70,140
• Factors of 26 - The factors of 26 are 1, 2, 13, 26
• Factors of 52 - The factors of 52 are 1, 2, 4, 13, 26, 52
• Factors of 13 - The factors of 13 are 1, 13
• Factors of 8 - The factors of 8 are 1, 2, 4, 8

Factors of 104 by Prime Factorization

Prime factorization of a number refers to breaking down the number into the form of products of its prime factors.

There are different methods that can be used for the prime factorization of a number.

Method 1: Division Method

To find the prime factors of 104 using the division method, follow these steps:

• Step 1. Start dividing 104 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number. 
• Step 2. After finding the smallest prime factor of the number 104, which is 2, divide 104 by 2 to obtain the quotient (52).

104 ÷ 2 = 52

• Step 3. Repeat step 1 with the obtained quotient (52). Again, the prime factor for 52 would be 2,

52 ÷ 2 = 26

Similarly,

26 ÷ 2 = 13

13 ÷ 13 = 1

So, the prime factorization of 104 is, 104 = 2 × 2 × 2 × 13 = 2³ × 13

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 104 as shown below:

So, the prime factorization of 104 is, 104 = 2 × 2 × 2 × 13 = 2³ × 13. Further, find the products of the multiplicands in different orders to obtain the composite factors of the number. Thus, all the factors of 104 can be written, including both the prime and composite numbers, as, 1, 2, 4, 8, 13, 26, 52, 104

Factors of 104 in Pairs

Pair factors of a number are two numbers which, when multiplied together, give that number. The pair factors of 104 would be the two numbers which, when multiplied, give 104 as the result. 

The following table represents the calculation of factors of 104 in pairs: 

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 104. They are called as negative pair factors.
Hence, the negative factor pairs of 104 would be ( -1, -104 ), ( -2, -52), ( -4, -26), and ( -8, -13).

Important Notes:

• Only whole numbers and integers can be factors.
• Only composite numbers can have more than two factors.
• The smallest factor of a number is 1 and the biggest factor of a number is the number itself.

FAQs on Factors of 104

Which is the samllest prime factor of 104?

The factors of 104 is 1, 2, 4, 8, 13, 26, 52, 104.
The smallest prime factor of 104 is 5.

Is 104 a perfect square?

We know that 104 = 2 × 2 × 2 × 13. Using prime factorization, we see that the square root of 104 cannot be calculated.
Thus, 104 is not a perfect square.

What are the factors of 104 and 105?

The factor of a number divides the number completely, i.e., leaves no remainder. The factors of 104 are 1, 2, 4, 8, 13, 26, 52, 104
The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105

What is the prime factorization of 104?

Prime factorization of a number refers to breaking down a number into the form of products of its prime factors.
So, the prime factorization of 104 is,  2 × 2 × 2 × 13 = 2³ × 13.

What are the factors of 104?

The factor of a number divides the number completely, i.e., leaves no remainder. The factors of 104 are 1, 2, 4, 8, 13, 26, 52, 104.