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factors

Factors of 78 | Factor Tree of 78 | Prime Factorization of 78 |

Written by Prerit Jain

Updated on: 15 Feb 2023

Factors of 78 | Factor Tree of 78 | Prime Factorization of 78 |

Factors of 78 | Factor Tree of 78 | Prime Factorization of 78 |

Factors are the numbers that can divide a given number leaving behind no remainders. There are both positive and negative factors for a number. Based on the count of the factors of a number, they can be grouped into prime numbers and composite numbers. Here, in this article, you can learn about the factors of 78 and the various methods to find its prime factors too.

What are the factors of 78?

The factors of the given number 78 are the numbers that can divide the given number 78 perfectly without having any decimal points in the quotient. The factors of a number can be divided into prime numbers and composite numbers. Prime numbers have either two or less than two numbers as their factors and composite numbers have more than two numbers as their factors. In this case, the factors of the given number are 1, 2, 3, 6, 13, 26, 39, and 78, so the number 78 is a composite number.

Factors of 78: 1, 2, 3, 6, 13, 26, 39, and 78
Negative Factors of 78: -1, -2, -3, -6, -13, -26, -39, and -78
Prime Factorization of 78: 2 x 3 x 13
Pair Factors of 78: (1, 78), (2, 39), (3, 26), and (6, 13)
Prime Factors of 78: 2, 3 and 13
Sum of Factors of 78: 168
Sum of Prime Factors of 78: 18
Factors of 78

What Are the Factors of 78 in Pairs?

The pair factors of a given number are the numbers that on multiplying with each other provide the given number. There are both positive and negative factors for a number.

Positive Pair Factors of 78

The positive pair factors of 78 are (1, 78), (2, 39), (3, 26), and (6, 13).

Positive Pair Factors of 78

Negative Pair Factors of 78

The negative factors of 78 are (-1, -78), (-2, -39), (-3, -26), and (-6, -13).

Negative Pair Factors of 78

What Is the Factor Tree of 78?

The prime factors of a number can be found using the factor tree method. The following are the steps that are involved in the factor tree method of 78:

  • Step 1: The number 78 is a multiple of 2 and 39, so let’s place them in the branches of the factor tree.
  • Step 2: Now, the number 39 is a product of the numbers 3 and 13 and so place 3 and 39 on the branches of 39.
  • Step 3: As the numbers 3 and 13 are prime numbers, we cant further make the branches. So, now let’s circle the prime numbers.

Therefore, the prime factors of 78 are 2 x 3 x 13. The image given below shows the factor tree of 78.

Factor tree of 78

How to Find Factors of 78 Through Division Method?

The division method is used to find the factors of the given number. In the division method, the given number is divided by the prime numbers in the numbering system until the quotient becomes 1. The following are the process involved in it:

  • 78 ÷ 1 = 78
  • 78 ÷ 2 = 39
  • 78 ÷ 3 = 26
  • 78 ÷ 6 = 13
  • 78 ÷ 13 = 6
  • 78 ÷ 26 = 3
  • 78 ÷ 39 = 2
  • 78 ÷ 78 = 1

Therefore, factors 78 are 1, 2, 3, 6, 13, 26, 39, and 78.

What Is the Basic Prime Factorization Method of 78?

Basic prime factorization is a method used to find the prime factors of a number. The methods involved in this process are given below:

  • Step 1: Let’s place the number 78 at the top, and divide it by the smallest prime number, which is 2.
    78 ÷ 2 = 39
  • Step 2: Now, the number 39 is divisible by 3.
    39 ÷ 3 = 13
  • Step 3: The number 13 is divisible by itself.
    13 ÷ 13 = 1
  • Step 4: Now, we have reached the remainder as 1 and it’s not further divisible.

Therefore, the prime factors 78 are 2, 3, and 13. The below image shows the Prime Factorization Method of 78.

Prime Factorization of 78

Solved Examples of 78

What is the sum of the factors of 78?
The sum of the factor of 78 is 168.

What are the prime factors of 78?
The prime factors of 78 are 2, 3, and 13.

What is the sum of the prime factors of 78?
The sum of the prime factors of 78 is 18.

What are the negative factors of 78?
The negative factors of 78 are -1, -2, -3, -6, -13, -26, -39, and -78.

Frequently Asked Questions

How do you find the prime factors of 78?
The prime factors of 78 can be found using the basic prime factorization method, factor tree method, and division method.

Is 78 a co-prime number?
Yes, the number 78 is a co-prime number as it has more than two factors.

What goes into 78 evenly?
The factors of the number 78 can divide that number evenly. Those numbers are 1, 2, 3, 6, 13, 26, 39, and 78.

What is the square of 78?
The square of 78 is 6084.

IS 78 in the 13 times table?
Yes, 13 is there in times table 78. As 13 x 6 = 78.

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Prerit Jain

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