Factors of 780: Prime Factorization, Methods, and Examples

780 is a composite number since it has twelve factors. It has 12 good qualities as well as 12 negative factors. These variables are all present on the number line and are all integers. The list of 780s contributing components is as follows:1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390 and 780.

By any of the numbers stated above, 580 can be divided in various ways.

Factors of 780

Here are the factors of number 780.

Factors of 780: 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390 and 780

Negative Factors of 780

The negative factors of 780 are similar to its positive aspects, just with a negative sign.

Negative Factors of 780: -1, -2,-3, -4, -5, -6, -10, -12, -13, -15, -20, -26, -30, -39, -52, -60, -65,-78, -130, -156, -195,- 260, -390 and -780

Prime Factorization of 780

The prime factorization of 780 is the way of expressing its prime factors in the product form.

Prime Factorization:  22 x 31 x 51 x 131

In this article, we will learn about the factors of 780 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 780?

The factors of 780 are 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390 and 780. These numbers are the factors as they do not leave any remainder when divided by 780.

The factors of 780 are classified as prime numbers and composite numbers. The prime factors of the number 780 can be determined using the prime factorization technique.

How To Find the Factors of 780?

You can find the factors of 780 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 780, create a list containing the numbers that are exactly divisible by 780 with zero remainders. One important thing to note is that 1 and 780 are the 780’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 780 are determined as follows:

$\dfrac{780}{1} = 780$

$\dfrac{780}{2} = 390$

$\dfrac{780}{3} = 230$

$\dfrac{780}{4} = 195$

$\dfrac{780}{5} = 156$

$\dfrac{780}{6} = 130$

$\dfrac{780}{10} = 78$

$\dfrac{780}{12} = 65$

$\dfrac{780}{13} = 60$

$\dfrac{780}{15} = 52$

$\dfrac{780}{20} = 39$

$\dfrac{780}{26} = 30$

$\dfrac{780}{30} = 26$

$\dfrac{780}{39} = 20$

$\dfrac{780}{52} = 15$

$\dfrac{780}{60} = 13$

$\dfrac{780}{65} = 12$

$\dfrac{780}{78} = 10$

$\dfrac{780}{130} = 6$

$\dfrac{780}{156} = 5$

$\dfrac{780}{195} = 4$

$\dfrac{780}{260} = 3$

$\dfrac{780}{390} = 2$

$\dfrac{780}{780} = 1$

Therefore,1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390 and 780 are the factors of 780.

Total Number of Factors of 780

For 780, there are 24 positive factors and 24 negative ones. So in total, there are 48 factors of 780.

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 780 is given as:

Factorization of 780 is 22 x 31 x 51 x 131.

The exponent of 2 is 2, 3 is 1, 5 is 1and 13 is 1.

Adding 1 to each and multiplying them together results in 48.

Therefore, the total number of factors of 780 is 48. 24 is positive, and 24 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 780 by Prime Factorization

The number 780 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 780 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 780, 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 780 can be expressed as:

780 = 22 x 31 x 51 x 131

Factors of 780 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 780, the factor pairs can be found as:

1 x 780 = 780

2 x390 = 780

3 x 260 = 780

4  x 195 = 780

5 x 156 = 780

6 x 130 = 780

10 x 78 = 780

12 x 65 = 780

13 x 60 = 780

15  x 52 = 780

20 x 39 = 780

26 x 30 = 780

The possible factor pairs of 780are given as (1, 780), (2, 390),(3, 260),(4, 195),(5, 156), (6, 130),(10, 78),(12, 65),(13, 60),(15, 52),(20, 39) ,and (26, 30).

All these numbers in pairs, when multiplied, give 780 as the product.

The negative factor pairs of 780 are given as:

-1 x -780 = 780

– 2 x -390 = 780

-3 x -260 = 780

-4  x -195 = 780

-5 x -156 = 780

-6 x -130 = 780

-10 x -78 = 780

-12 x -65 = 780

-13 x -60 = 780

-15  x -52 = 780

-20 x -39 = 780

-26 x -30 = 780

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, -10, -12, -13, -15, -20, -26, -30, -39, -52, -60, -65,-78, -130, -156, -195,- 260, -390 and -780 are called negative factors of 780.

The list of all the factors of 780, including positive as well as negative numbers, is given below.

Factor list of 780: 1,-1, 2,-2,3,-3,4, -4,5, -5,6, -6,10, -10, 12,-12, 13,-13,15, -15,20. -20, 26,-26,30, -30,39, -39,52, -52,60, -60, 65,-65,78,-78, 130,-130, 156,-156,195, -195,260,-260,390, -390 and 780,-780

Factors of 780 Solved Examples

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

Example 1

How many factors of 780 are there?

Solution

The total number of Factors of 780 is 48.

Factors of 780 are 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390 and 780.

Example 2

Find the factors of 780 using prime factorization.

Solution

The prime factorization of 780 is given as:

780 $\div$ 2 = 390

390 $\div$ 2 = 195

195 $\div$ 3 = 65

65 $\div$ 5 = 13

13 $\div$ 13 = 1

So the prime factorization of 780 can be written as:

22 x 31 x 51 x 131 = 780