Factors of 417

The numbers that divide 417 evenly are known as factors of 417.

A factor of 417 is a number that divides the number without remainder.

The factors of 417 are 1, 3, 139, and 417.

Negative factors of 417: -1, -3, -139, and -417.

Prime factors of 417: 3 and 139.

Prime factorization of 417: 3 × 139.

The sum of factors of 417: 1 + 3 + 139 + 417 = 560.

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

• Finding factors using multiplication
   
• Finding factors using 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 417. Identifying the numbers which are multiplied to get the number 417 is the multiplication method.

Step 1: Multiply 417 by 1, 417 × 1 = 417.

Step 2: Check for other numbers that give 417 after multiplying 3 × 139 = 417 Therefore, the positive factor pairs of 417 are: (1, 417), (3, 139). All these factor pairs result in 417.

For every positive factor, there is a negative factor.

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

Step 1: Divide 417 by 1, 417 ÷ 1 = 417.

Step 2: Continue dividing 417 by the numbers until the remainder becomes 0. 417 ÷ 1 = 417 417 ÷ 3 = 139

Therefore, the factors of 417 are: 1, 3, 139, 417.

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 factor tree

Using Prime Factorization: In this process, prime factors of 417 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1. 417 ÷ 3 = 139 139 ÷ 139 = 1

The prime factors of 417 are 3 and 139.

The prime factorization of 417 is: 3 × 139.

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

Step 1: Firstly, 417 is divided by 3 to get 139.

Step 2: Now divide 139 by 139 to reach 1. Here, 139 is the smallest prime number and cannot be divided anymore. So, the prime factorization of 417 is: 3 × 139.

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 417: (1, 417), (3, 139).

Negative factor pairs of 417: (-1, -417), (-3, -139).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 417 are 1, 3, 139, and 417.
   
• Prime factors: The factors which are prime numbers. For example, 3 and 139 are prime factors of 417.
   
• 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 417 are (1, 417), (3, 139).
   
• Prime factorization: Expressing a number as a product of its prime factors. For example, the prime factorization of 417 is 3 × 139.
   
• Multiplication method: A method to find factors by checking pairs of numbers that multiply to the target number. For example, finding the pairs for 417.