Factors of 720: Prime Factorization, Methods, and Examples

The factors of 720 are the numbers that leave no residue when divided by 720. The actual number’s components are the numbers that divide it in half ultimately. 

The article provides additional information regarding the factorization of 720.

Factors of 720

Here are the factors of number 720.

Factors of 720: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360 and 720

Negative Factors of 720

The negative factors of 720 are similar to its positive aspects, just with a negative sign.

Negative Factors of 720: -1, -2, -3, -4, -5, -6, -8, -9, -10, -12, -15, -16, -18, -20, -24, -30, -36, -40, -45, -48,- 60, -72,- 80, -90, -120, -144, -180, -240, -360 and -720

Prime Factorization of 720

The prime factorization of 720 is the way of expressing its prime factors in the product form.

Prime Factorization: 2⁴ x 3² x 5

In this article, we will learn about the factors of 720 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 720?

The factors of 720 are a, b, c, and 720. These numbers are the factors as they do not leave any remainder when divided by 720.

The factors of 720 are classified as prime numbers and composite numbers. The prime factors of the number 720 can be determined using the prime factorization technique.

How To Find the Factors of 720?

You can find the factors of 720 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 720, create a list containing the numbers that are exactly divisible by 720 with zero remainders. One important thing to note is that 1 and 720 are the 720’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 720 are determined as follows:

\[\dfrac{ 720}{1} = 720\]

\[\dfrac{ 720}{2} = 360\]

\[\dfrac{ 720}{3} = 240\]

\[\dfrac{ 720}{ 4} = 180\]

\[\dfrac{ 720}{5} = 144\]

\[\dfrac{ 720}{6} = 120\]

\[\dfrac{ 720}{8} = 90\]

\[\dfrac{ 720}{ 9} = 180\]

\[\dfrac{ 720}{10} = 72\]

\[\dfrac{ 720}{12} = 60\]

\[\dfrac{ 720}{15} = 48\]

\[\dfrac{ 720}{ 16} = 45\]

\[\dfrac{ 720}{18} = 40\]

\[\dfrac{ 720}{20} = 36\]

\[\dfrac{ 720}{24} = 30\]

\[\dfrac{ 720}{ 30} = 24\]

\[\dfrac{ 720}{36} = 20\]

\[\dfrac{ 720}{40} = 18\]

\[\dfrac{ 720}{45} = 16\]

\[\dfrac{ 720}{ 48} = 15\]

\[\dfrac{ 720}{60} = 12\]

\[\dfrac{ 720}{72} = 10\]

\[\dfrac{ 720}{80} = 9\]

\[\dfrac{ 720}{ 90} = 8\]

\[\dfrac{ 720}{120} = 6\]

\[\dfrac{ 720}{144} =  5\]

\[\dfrac{ 720}{180} = 4\]

\[\dfrac{ 720}{ 240} = 3\]

\[\dfrac{ 720}{360} = 2\]

\[\dfrac{ 720}{720} = 1\]

Therefore, 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360 and 720 are the factors of 720.

Total Number of Factors of 720

For 720, there are 30 positive factors and 30 negative ones. So in total, there are 60 factors of 720. 

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 720 is given as:

Factorization of 720 is 2⁴ x 3² x 5.

The exponent of 2 is 4, 3 is 2, and 5 is 1.

Adding 1 to each and multiplying them together results in 60.

Therefore, the total number of factors of 720 is 60. 30 are positive, and 30 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 720 by Prime Factorization

The number 720 is a composite 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 X 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 720, 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 720 can be expressed as:

 720 = 2⁴ x 3² x 5

Factors of 720 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 720, the factor pairs can be found as:

1 x 720 = 720

2 x 360= 720

3 x 240 = 720

4 x 180= 720

5 x 144= 720

6 x 120 = 720

8 x 90= 720

9 x 80 = 720

10 x 72= 720

12 x 60= 720

15 x 48 = 720

16 x 45= 720

18 x 40 = 720

20 x 36= 720

24 x 30= 720

The possible factor pairs of 720 are given as (1, 720),(2, 360),(3, 240),(4, 180),(5, 144),(6, 120),(8, 90),(9, 80),(10, 72),(12, 60),(15, 48),(16, 45),(18, 40),(20, 36), and (24, 30).

All these numbers in pairs, when multiplied, give 720 as the product.

The negative factor pairs of 720 are given as:

-1 x -720 = 720

-2 x -360= 720

-3 x -240 = 720

-4 x -180= 720

-5 x -144= 720

-6 x -120 = 720

-8 x -90= 720

-9 x -80 = 720

-10 x -72= 720

-12 x -60= 720

-15 x -48 = 720

-16 x -45= 720

-18 x -40 = 720

-20 x -36= 720

-24 x -30= 720

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, -4, -5, -6, -8, -9, -10, -12, -15, -16, -18, -20, -24, -30, -36, -40, -45, -48,- 60, -72,- 80, -90, -120, -144, -180, -240, -360 and -720 are called negative factors of 720.

The list of all the factors of 720, including positive as well as negative numbers, is given below.

Factor list of 720: 1,-1, 2,-2, 3,-3, 4,-4, 5,-5, 6,-6, 8,-8, 9,-9, 10,-10, 12,-12, 15,-15, 16,-16, 18,-18, 20,-20, 24,-24, 30,-30, 36,-36, 40,-40, 45,-45, 48,-48,60,-60, 72,-72,80,-80,90, -90, 120,-120, 144,-144,180, -180, 240,-240, 360,-360, 720, and – 720

Factors of 720 Solved Examples

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

Example 1

How many factors of 720 are there?

Solution

The total number of Factors of 720 is 60.

Factors of 720 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360 and 720.

Example 2

Find the factors of 720 using prime factorization.

Solution

The prime factorization of 720 is given as:

 720 $\div$ 2 = 360

360 $\div$ 2 = 180 

 180 $\div$ 2 = 90 

90 $\div$ 2 = 45 

 45 $\div$ 3 = 15

15 $\div$ 3 = 5

5 $\div$ 5= 1 

So the prime factorization of 720 can be written as:

2⁴ x 3² x 5 = 720