Factors of 462

The numbers that divide 462 evenly are known as factors of 462.

A factor of 462 is a number that divides the number without a remainder.

The factors of 462 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, and 462.

Negative factors of 462: -1, -2, -3, -6, -7, -11, -14, -21, -22, -33, -42, -66, -77, -154, -231, and -462.

Prime factors of 462: 2, 3, 7, and 11.

Prime factorization of 462: 2 × 3 × 7 × 11.

The sum of factors of 462: 1 + 2 + 3 + 6 + 7 + 11 + 14 + 21 + 22 + 33 + 42 + 66 + 77 + 154 + 231 + 462 = 1160

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 462. Identifying the numbers which are multiplied to get the number 462 is the multiplication method.

Step 1: Multiply 462 by 1, 462 × 1 = 462.

Step 2: Check for other numbers that give 462 after multiplying:

2 × 231 = 462
3 × 154 = 462
6 × 77 = 462
7 × 66 = 462
11 × 42 = 462
14 × 33 = 462
21 × 22 = 462

Therefore, the positive factor pairs of 462 are: (1, 462), (2, 231), (3, 154), (6, 77), (7, 66), (11, 42), (14, 33), (21, 22).

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 the simple division method:

Step 1: Divide 462 by 1, 462 ÷ 1 = 462.

Step 2: Continue dividing 462 by the numbers until the remainder becomes 0.

462 ÷ 1 = 462
462 ÷ 2 = 231
462 ÷ 3 = 154
462 ÷ 6 = 77
462 ÷ 7 = 66
462 ÷ 11 = 42
462 ÷ 14 = 33
462 ÷ 21 = 22

Therefore, the factors of 462 are: 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462.

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

462 ÷ 2 = 231
231 ÷ 3 = 77
77 ÷ 7 = 11
11 ÷ 11 = 1

The prime factors of 462 are 2, 3, 7, and 11.

The prime factorization of 462 is: 2 × 3 × 7 × 11.

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

Step 1: Firstly, 462 is divided by 2 to get 231.

Step 2: Now divide 231 by 3 to get 77.

Step 3: Then divide 77 by 7 to get 11. Here, 11 is the smallest prime number that cannot be divided anymore.

So, the prime factorization of 462 is: 2 × 3 × 7 × 11.

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 462: (1, 462), (2, 231), (3, 154), (6, 77), (7, 66), (11, 42), (14, 33), (21, 22).

Negative factor pairs of 462: (-1, -462), (-2, -231), (-3, -154), (-6, -77), (-7, -66), (-11, -42), (-14, -33), (-21, -22).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 462 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, and 462.
   
• Prime factors: The factors which are prime numbers. For example, 2, 3, 7, and 11 are prime factors of 462.
   
• 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 462 are (1, 462), (2, 231), etc.
   
• Prime factorization: Breaking down a number into a product of its prime factors. For 462, this is 2 × 3 × 7 × 11.
   
• Multiplication method: A technique to find factors by identifying pairs of numbers that multiply to give the original number. For 462, examples include (21, 22) and (7, 66).