Factors

# Factors of 130 | Prime Factorization of 130 | Factor Tree of 130

Written by Prerit Jain

Updated on: 21 Jun 2023

## Factors of 130

Calculate Factors of

The Factors are

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## What are the factors of 130

The factors of a given number are the numbers that can divide the given number entirely with no decimal digits in the quotient and zero remainders. To find the factors of 130, we can start by making a list of all of the numbers that can be divided into 130 evenly.

Here is the list of factors of 130: 1, 2, 5, 10, 13, 26, 65 and 130.

## How to Find Factors of 130

The methods through which you can find the factors of 130 are as follows:

• Factors of 130 using the Multiplication Method
• Factors of 130 using the Division Method
• Prime Factorization of 130
• Factor tree of 130

## Factors of 130 Using the Multiplication Method

The multiplication method is a way to find the factors of a number by multiplying pairs of numbers together. To use this method to find the factors of 130, we can list all of the numbers that can be multiplied together to get 130. We can start with the number 1 and work our way up.

Here is the list of factors of 130 using the multiplication method:

1 x 130 = 130
2 x 65 = 130
5 x 26 = 130
10 x 13 = 130

In this case, the factors of 130 using the multiplication method are 1, 2, 5, 10, 13, 26, and 65. These are the only numbers that can be multiplied together to get 130.

## Factors of 130 Using the Division Method

The division method is a way to find the factors of a number by dividing the number by different numbers and seeing if there is a remainder. To find the factors of 130 using the division method, we can divide 130 by each number to see if there is a remainder. If there is no remainder, then the number is a factor of 130.

Here is the list of all of the factors of 130 using the division method:

130 ÷ 1 = 130 (no remainder)
130 ÷ 2 = 65 (no remainder)
130 ÷ 5 = 26 (no remainder)
130 ÷ 10 = 13 (no remainder)
130 ÷ 13 = 10 (no remainder)
130 ÷ 26 = 5 (no remainder)
130 ÷ 65 = 2 (no remainder)
130 ÷ 130 = 1 (no remainder)

Since there is no remainder when we divide 130 by any of these numbers, they are all factors of 130. This means that 1, 2, 5, 10, 13, 26, 65, and 130 are the only numbers that can be divided into 130 evenly, with no remainder.

## Prime Factorization of 130

Calculate Prime Factors of

The Prime Factors of 130 =

2 x

5 x

13

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The prime factorization of a number is a way to express that number as a product of prime numbers. Prime numbers are numbers that are only divisible by 1 and themselves, such as 2, 3, 5, and 7. To find the prime factorization of 130, we can divide it by different prime numbers and see if any of them are factors.

To find the prime factorization of 130, we can start by dividing it by the smallest prime number, which is 2. 130 divided by 2 is 65 with a remainder of 0, so 2 is a factor of 130. We can then divide 130 by 2 again to get 65 with a remainder of 0, which means that 2 is a factor of 130 again. We can continue this process until we reach a number that is not divisible by 2 anymore.

In this case, the prime factorization of 130 is 2 x 2 x 5 x 13 because these are the prime numbers that can be multiplied together to get 130. This means that 130 can be expressed as the product of the prime numbers 2, 2, 5, and 13.

## Factor tree of 130

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A factor tree is a diagram that shows how a number can be broken down into smaller factors until only prime numbers are left. To create a factor tree for 130, we can start by looking for a factor of 130. The smallest prime number that is a factor of 130 is 2, so we can write 2 on the tree and divide 130 by 2 to get 65:

130 65

65 is not a prime number, so we can continue to divide it by smaller numbers until we reach a prime number. The next smallest prime number that is a factor of 65 is 5, so we can write 5 on the tree and divide 65 by 5 to get 13:

130 5

/

65 13

13 is a prime number, so we can stop here and the factor tree for 130 is complete:

130 5

/

65 13

The prime factorization of 130 is the list of prime numbers that can be multiplied together to get 130. In this case, the prime factorization of 130 is 2 x 5 x 13, because these are the prime numbers that were used to create the factor tree. This means that 130 can be expressed as the product of the prime numbers 2, 5, and 13.

## Factor Pairs of 130

Calculate Pair Factors of

1 x 130=130

2 x 65=130

5 x 26=130

10 x 13=130

13 x 10=130

26 x 5=130

65 x 2=130

So Pair Factors of 130 are

(1,130)

(2,65)

(5,26)

(10,13)

(13,10)

(26,5)

(65,2)

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Factor pairs are pairs of numbers that can be multiplied together to get a specific number. For example, the factor pairs of 12 are (1, 12), (2, 6), and (3, 4), because these pairs of numbers can be multiplied together to get 12.

To find the factor pairs of 130, we can start by making a list of all of the factors of 130. The factors of 130 are 1, 2, 5, 10, 13, 26, 65, and 130. We can then pair each of these numbers with every other number in the list to create all of the possible factor pairs of 130.

Here is the list of all of the factor pairs of 130: (1, 130), (2, 65), (5, 26), (10, 13), (13, 10), (26, 5), (65, 2) and (130, 1).

## Factors of 130 – Quick Recap

• Factors of 130:  1, 2, 5, 10, 13, 26, 65, and 130
• Negative Factors of 130:    -1, -2, -5, -10, -13, -26, -65, and -130.
• Prime Factors of 130: 2, 5, and 13.
• Prime Factorization of 130:  2, 5, and 13.

## Solved Examples of Factor of 130

Q.1: Joe needs to buy 130 books for his classroom. If each book cost \$7, how much money must he spend?
Solution: Total cost = Number of books * Cost per book Total cost = 130 * \$7 = \$910. So, Joe must spend \$910 to buy 130 books for his classroom.

Q.2: Maria has a box containing 10 items and wishes to give an equal number of items away. How many items should she give away?
Solution: Number of items to give away = Total number of items / Number of recipients Number of items to give away = 10 / N.

Q.3: Mary needs to find the greatest common factor (GCF) for 130 and 165. What is it?
Solution: Factors of 130: 1, 2, 5, 10, 13, 26, 65, 130. Factors of 165: 1, 3, 5, 11, 15, 33, 55, 165. The largest common factor is 5.

Q.4: Anna has 260 marbles that she wants to divide equally between her 4 brothers, How many marbles would each brother get?
Solution: 260 marbles / 4 brothers = 65 marbles per brother. Therefore, each brother would get 65 marbles from Anna’s collection.

Q.5: John wants to display 130 photos in an album but only has space for 50 photos per page, how many pages will he need in total?
Solution: 130 photos / 50 photos per page = 2.6 pages. Since we can’t have a fraction of a page, we round up to the nearest whole number. Therefore, John will need a total of 3 pages to display all 130 photos in his album.

Q.6: Alex has 190 candies that he wants to share with 19 friends, how many pieces of candy will each friend receive?
Solution: 190 candies / 19 friends = 10 candies per friend. Each friend will receive 10 pieces of candy.

Q.7: Bryan is arranging chairs into rows for a theatre performance and needs 13 chairs per row, if he has 104 chairs in total, how many rows can be created?
Answer: 104 chairs / 13 chairs per row = 8 rows. Bryan can create 8 rows with the given number of chairs.

Q.8: Bethany wants to make 6 presents for her family members using individual items from her toy box containing 65 toys, what is the greatest number of different presents she can make with these toys?
Solution: Since Bethany has 65 toys and wants to make 6 presents, she can use up to 65 toys for the first present, 64 toys for the second present (one toy has already been used for the first present), 63 toys for the third present, and so on. Therefore, the greatest number of different presents Bethany can make with the 65 toys is 65 + 64 + 63 + 62 + 61 + 60 = 375. Bethany can make a maximum of 375 different presents using the toys from her toy box.

Q.9: Sam needs to purchase 132 books from a store where each book costs \$10, how much will it cost him altogether?
Solution:
Total cost = Number of books × Cost per book Total cost = 132 × \$10. Calculating the total cost: Total cost = \$1320. Therefore, it will cost Sam \$1320 altogether to purchase 132 books from the store.

## Frequently Asked Questions on Factors of 130

### What are the factors of 130?

The factors of 130 are 1, 2, 5, 10, 13, 26, 65, and 130.

### What is the greatest common factor (GCF) for 130 and 160?

The greatest common factor (GCF) of 130 and 160 is 10.

### How do you find the prime factors of 130?

The prime factor of 130 is 2 x 5 x 13.

### How many divisors does the number 130 have?

The number 130 has 8 divisors 1, 2, 5, 10, 13, 26, 65, and 130.

### Can you use division to find out if a number is a factor of another number?

Yes – if a division operation between two numbers yields no remainder then that means the second number was a factor of the first one. For example, to know if 7 is a factor of 130, we can divide it and check that the result has no remainder – which it indeed doesn’t(130 divided by 7 equals 18). Thus we know 7 is one of the factors of 130.

### Are there any perfect squares between 128 and 132?

There are no perfect squares between 128 and 132.

### What is the HCF or GCD for 125 and 131?

Both 125 and 131 are prime numbers, which means they do not have any common factors other than 1. Therefore, the HCF/GCD of 125 and 131 is 1.

### If someone needed to purchase 1300 books from a store, how much would they need to spend if each book costs \$7?

Number of books: 1300 Cost per book: \$7. Total cost = Number of books × Cost per book = 1300 × \$7 = \$9100.
Therefore, if someone needed to purchase 1300 books from a store, they would need to spend \$9100.

Written by by

Prerit Jain

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