Factors of 430

The numbers that divide 430 evenly are known as factors of 430.

A factor of 430 is a number that divides the number without remainder.

The factors of 430 are 1, 2, 5, 10, 43, 86, 215, and 430.

Negative factors of 430: -1, -2, -5, -10, -43, -86, -215, and -430.

Prime factors of 430: 2, 5, and 43.

Prime factorization of 430: 2 × 5 × 43.

The sum of factors of 430: 1 + 2 + 5 + 10 + 43 + 86 + 215 + 430 = 792

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 430. Identifying the numbers which are multiplied to get the number 430 is the multiplication method.

Step 1: Multiply 430 by 1, 430 × 1 = 430.

Step 2: Check for other numbers that give 430 after multiplying

2 × 215 = 430

5 × 86 = 430

10 × 43 = 430

Therefore, the positive factor pairs of 430 are: (1, 430), (2, 215), (5, 86), (10, 43).

All these factor pairs result in 430.

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 as whole numbers as factors. Factors can be calculated by following a simple division method -

Step 1: Divide 430 by 1, 430 ÷ 1 = 430.

Step 2: Continue dividing 430 by the numbers until the remainder becomes 0.

430 ÷ 1 = 430

430 ÷ 2 = 215

430 ÷ 5 = 86

430 ÷ 10 = 43

Therefore, the factors of 430 are: 1, 2, 5, 10, 43, 86, 215, 430.

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 430 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

430 ÷ 2 = 215

215 ÷ 5 = 43

43 ÷ 43 = 1

The prime factors of 430 are 2, 5, and 43. The prime factorization of 430 is: 2 × 5 × 43.

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

Step 1: Firstly, 430 is divided by 2 to get 215.

Step 2: Now divide 215 by 5 to get 43.

Step 3: Here, 43 is a prime number and cannot be divided anymore.

So, the prime factorization of 430 is: 2 × 5 × 43.

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 430: (1, 430), (2, 215), (5, 86), (10, 43).

Negative factor pairs of 430: (-1, -430), (-2, -215), (-5, -86), (-10, -43).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 430 are 1, 2, 5, 10, 43, 86, 215, and 430.
   
• Prime factors: The factors which are prime numbers. For example, 2, 5, and 43 are prime factors of 430.
   
• 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 430 are (1, 430), (2, 215), etc.
   
• Prime Factorization: The process of determining the prime numbers that multiply together to give the original number. For example, the prime factorization of 430 is 2 × 5 × 43.
   
• Multiples: Multiples of a number are the product of that number and any integer. For example, 2, 4, 6, 8, etc., are multiples of 2.