# Factors of 462

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

#### How to find factors of a number

 1.   Find factors of 462 using Division Method 2.   Find factors of 462 using Prime Factorization 3.   Find factors of 462 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 462

• Divide 462 by 1: 462 ÷ 1 : Remainder = 0
• Divide 462 by 2: 462 ÷ 2 : Remainder = 0
• Divide 462 by 3: 462 ÷ 3 : Remainder = 0
• Divide 462 by 6: 462 ÷ 6 : Remainder = 0
• Divide 462 by 7: 462 ÷ 7 : Remainder = 0
• Divide 462 by 11: 462 ÷ 11 : Remainder = 0
• Divide 462 by 14: 462 ÷ 14 : Remainder = 0
• Divide 462 by 21: 462 ÷ 21 : Remainder = 0
• Divide 462 by 22: 462 ÷ 22 : Remainder = 0
• Divide 462 by 33: 462 ÷ 33 : Remainder = 0
• Divide 462 by 42: 462 ÷ 42 : Remainder = 0
• Divide 462 by 66: 462 ÷ 66 : Remainder = 0
• Divide 462 by 77: 462 ÷ 77 : Remainder = 0
• Divide 462 by 154: 462 ÷ 154 : Remainder = 0
• Divide 462 by 231: 462 ÷ 231 : Remainder = 0
• Divide 462 by 462: 462 ÷ 462 : Remainder = 0

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

#### 2. Steps to find factors of 462 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 462 using the division method, follow these steps:

• Step 1. Start dividing 462 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 462, which is 2. Divide 462 by 2 to obtain the quotient (231).
462 ÷ 2 = 231
• Step 3. Repeat step 1 with the obtained quotient (231).
231 ÷ 3 = 77
77 ÷ 7 = 11
11 ÷ 11 = 1

So, the prime factorization of 462 is, 462 = 2 x 3 x 7 x 11.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 462 as shown below:

So, the prime factorization of 462 is, 462 = 2 x 3 x 7 x 11.

#### 3. Find factors of 462 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 462 would be the two numbers which, when multiplied, give 462 as the result.

The following table represents the calculation of factors of 462 in pairs:

Factor Pair Pair Factorization
1 and 462 1 x 462 = 462
2 and 231 2 x 231 = 462
3 and 154 3 x 154 = 462
6 and 77 6 x 77 = 462
7 and 66 7 x 66 = 462
11 and 42 11 x 42 = 462
14 and 33 14 x 33 = 462
21 and 22 21 x 22 = 462

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 462. They are called negative pair factors.

Hence, the negative pairs of 462 would be ( -1 , -462 ) , ( -2 , -231 ) , ( -3 , -154 ) , ( -6 , -77 ) , ( -7 , -66 ) , ( -11 , -42 ) , ( -14 , -33 ) and ( -21 , -22 ) .

#### How do you explain factors?

In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 462 is a factor of itself.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462 are exact divisors of 462.
• 1 is a factor of every number. Eg. 1 is a factor of 462.
• Every number is a factor of zero (0), since 462 x 0 = 0.

• What are the prime factors of 462?

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

• What two numbers make 462?

Two numbers that make 462 are 2 and 231.

• What is the greatest prime factors of 462?

The greatest prime factor of 462 is 11.

• What are factors of 462?

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

• How do you find factors of a negative number? ( eg. -462 )?

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

• What are five multiples of 462?

First five multiples of 462 are 924, 1386, 1848, 2310, 2772.

• Write some multiples of 462?

First five multiples of 462 are 924, 1386, 1848, 2310.

• Is 462 a perfect square?

No 462 is not a perfect square.

• What two numbers make 462?

Two numbers that make 462 are 2 and 231.

#### Examples of Factors

What is prime factorization of 462?

Prime factorization of 462 is 2 x 3 x 7 x 11 = 2 x 3 x 7 x 11.

Sammy is puzzled while calculating the prime factors of 462. Can you help him find them?

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

Kevin has been asked to write 15 factor(s) of 462. Can you predict the answer?

15 factor(s) of 462 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231.

Joey wants to write all the prime factors of 462 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 462 are 2, 3, 7, 11.
So in exponential form it can be written as 2 x 3 x 7 x 11.

How many factors are there for 462?

Factors of 462 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462.
So there are in total 16 factors.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 462? Help her in writing all the factors.

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

Can you help Rubel to find out the product of the even factors of 462?

Factors of 462 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462.
Even factors of 462 are 2, 6, 14, 22, 42, 66, 154, 462.
Hence, product of even factors of 462 is; 2 x 6 x 14 x 22 x 42 x 66 x 154 x 462 = 728933458176.