Factors of 290

The numbers that divide 290 evenly are known as factors of 290.

A factor of 290 is a number that divides the number without a remainder.

The factors of 290 are 1, 2, 5, 10, 29, 58, 145, and 290.

Negative factors of 290: -1, -2, -5, -10, -29, -58, -145, and -290.

Prime factors of 290: 2, 5, and 29.

Prime factorization of 290: 2 × 5 × 29.

The sum of factors of 290: 1 + 2 + 5 + 10 + 29 + 58 + 145 + 290 = 540

Factors can be found using different methods. Mentioned below are some commonly used methods:

• Finding factors using multiplication
  
   
• Finding factors using the division method
  
   
• Prime factors and prime factorization

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 290. Identifying the numbers which are multiplied to get the number 290 is the multiplication method.

Step 1: Multiply 290 by 1, 290 × 1 = 290.

Step 2: Check for other numbers that give 290 after multiplying

2 × 145 = 290

5 × 58 = 290

10 × 29 = 290

Therefore, the positive factor pairs of 290 are: (1, 290), (2, 145), (5, 58), (10, 29).

All these factor pairs result in 290. For every positive factor, there is a negative factor.

Dividing the given numbers with the whole numbers until the remainder becomes zero and listing out the numbers which result in whole numbers as factors. Factors can be calculated by following a simple division method -

Step 1: Divide 290 by 1, 290 ÷ 1 = 290.

Step 2: Continue dividing 290 by the numbers until the remainder becomes 0.

290 ÷ 1 = 290

290 ÷ 2 = 145

290 ÷ 5 = 58

290 ÷ 10 = 29

Therefore, the factors of 290 are: 1, 2, 5, 10, 29, 58, 145, 290.

The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:

• Using prime factorization
   
• Using a factor tree

Using Prime Factorization: In this process, prime factors of 290 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

290 ÷ 2 = 145

145 ÷ 5 = 29

29 ÷ 29 = 1

The prime factors of 290 are 2, 5, and 29.

The prime factorization of 290 is: 2 × 5 × 29.

The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show -

Step 1: Firstly, 290 is divided by 2 to get 145.

Step 2: Now divide 145 by 5 to get 29.

Step 3: Divide 29 by 29 to get 1. Here, 29 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 290 is: 2 × 5 × 29.

Factor Pairs Two numbers that are multiplied to give a specific number are called factor pairs.

Both positive and negative factors constitute factor pairs.

Positive factor pairs of 290: (1, 290), (2, 145), (5, 58), and (10, 29).

Negative factor pairs of 290: (-1, -290), (-2, -145), (-5, -58), and (-10, -29).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 290 are 1, 2, 5, 10, 29, 58, 145, and 290.
  
   
• Prime factors: The factors which are prime numbers. For example, 2, 5, and 29 are prime factors of 290.
  
   
• Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 290 are (1, 290), (2, 145), etc.
  
   
• Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 290 is 2 × 5 × 29.
  
   
• Multiple: A number that can be divided by another number without leaving a remainder. For example, 290 is a multiple of 29.