Factors of 12

Factors of 12 are 1, 2, 3, 4, 6, and 12. Factors of any number are the numbers that can be multiplied together to give the result of the number itself. In other words, Factors of a number are integers that divide that number without leaving a remainder. In the case of 12, 1, 2, 3, 4, 6, and 12 are factors as these numbers can divide 12 without leaving any remainder.

In this article, we will answer the questions such as “What are Factors?”, “What are some Factors of 12?”, and “How to Find Factors of 12?”. So let’s start learning about Factors of 12.

Factor Definition

Factors are the numbers that multiply together to result in a given number.

In simpler words, a factor of a number is a whole number that divides the given number without leaving a remainder. For the number 12, each of the factors of 12 are the integers that can evenly divide it and there is no remainder left on the division of 12 with it’s factor.

What are the Factors of 12?

The factors of 12 are the numbers that can be multiplied together to give the product 12. In the case of 12, the factors are 1, 2, 3, 4, 6 and 12. These numbers can be multiplied in pairs to equal 12:

• 1 × 12 = 12
• 2 × 6 = 12
• 3 × 4 = 12

So, these are the factors of 12: 1, 2, 3, 4, 6 and 12.

List of All Factors of 12

Here is a list of all the factors of 12:

Factors of 12 are 1, 2, 3, 4, 6, and 12

Prime Factors of 12

The prime factors of 12 are the prime numbers that multiply together to give 12. For the number 12, these prime factors are:

• 2 (since 2 is a prime number and 12 is divisible by 2)
• 3 (since 3 is a prime number and 12 is divisible by 3)

When expressed as a product of prime factors, 12 is written as 2² × 3. This is because 12 can be divided into 2 × 2 × 3, where 2 appears twice (hence 2²) and 3 appears once.

How to Find Factors of 12?

To find the factors of 12, you need to identify all the whole numbers that can divide 12 without leaving a remainder.

1. Start with 1: Since 1 multiplied by any number gives that number, 1 and 12 are a pair of factors. So, 1 and 12 are factors of 12.
2. Try the next number, 2: Does 2 multiply with another whole number to give 12? Yes, 2 × 6 = 12. So, 2 and 6 are factors of 12.
3. Try 3: We find that 3 × 4 = 12, so 3 and 4 are factors of 12.
4. Try 4: We’ve already found this in the previous step, so no need to repeat.
5. Continue with 5, 6, etc.: Once you reach a number that you’ve already listed as a factor, you can stop. In this case, we stop after 4, as 5 does not divide 12 evenly and 6 is already listed.

So, the factors of 12 are 1, 2, 3, 4, 6, and 12.

Prime Factorization of 12

Prime Factorization is a method of factoring any number using prime numbers because any number can be expressed as the product of primes. To find the prime factorization of 12, you can begin by dividing it by the smallest prime number, which is 2, and continue dividing until further division is not possible, as follows:

Step 1: Start with 12.

Step 2: Divide by 2: 12 ÷ 2 = 6.

Step 3: Divide by 2 again: 6 ÷ 2 = 3.

Step 4: Divide by 3: 3 ÷ 3 = 1

Read More about Prime Factorization.

Factor Tree of 12

A factor tree is a diagram that breaks down a number into its prime factors. Here’s a factor tree for the number 12:

Factors of 12 in a Tree-like Representation

Factor Pairs of 12

Factor pairs of 12 are pairs of numbers that, when multiplied together, equal 12. These pairs can be positive as well as negative.

Positive Factor Pairs of 12

Positive factor pairs of 12 are:

• 1 × 12 = 12
• 2 × 6 = 12
• 3 × 4 = 12

Each pair consists of two factors of 12.

Negative Factor Pairs of 12

Negative factor pairs of 12 are:

• (-1) × (-12) = 12
• (-2) × (-6) = 12
• (-3) × (-4) = 12

Each negative pair consists of two negative factors of 12.

Solved Examples on Factors of 12

Example 1: What is the sum of all the factors of 12?

Solution:

The factors of 12 are 1, 2, 3, 4, 6, and 12.

Sum of the factors of 12 = 1 + 2 + 3 + 4 + 6 + 12

Sum of the factors of 12 = 28

Example 2: If b is a factor of 12 and b > 1, What is the largest possible value of b?

Solution:

The factors of 12 are 1, 2, 3, 4, 6, and 12.

The largest factor of 12, other than 1 and 12,

= 6

Example 3: Find two factors of 12 whose product is equal to 12.

Solution:

Listed are the factors of 12 are 1, 2, 3, 4, 6, and 12.

Two factors of 12 whose product is 12 are:

3 and 4

as 3×4=12

Example 4: If d is a factor of both 12 and 6, what are the possible values of d?

Solution:

We know the factors of 12 are 1, 2, 3, 4, 6, and 12.

We know the factors of 6 are 1, 2, 3 and 6.

The common factors of 12 and 6 are 1, 2, 3, and 6

Example 5: Express 12 as the product of its prime factors.

Solution:

12 expressed as the prime factorization of 12 is

= 2² ×3

Practice Problems on Factors of 12

Problem 1: What is the product of all the factors of 12?

Problem 2: If b is a factor of 12 and b > 1, what is the smallest possible value of b?

Problem 3: Find two factors of 12 whose product is equal to 6.

Problem 4: If d is a factor of both 12 and 10, what are the possible values of d?

Problem 5: Find two factors of 12 whose product is equal to 8.

FAQs on Factors of 12

1. What are the Factors of 12?

Factors of 12: 1, 2, 3, 4, 6 and 12.

2. How many Factors does 12 have?

The number 12 has a total of six factors: 1, 2, 3, 4, 6, and 12.

3. What is the Factor Tree of 12?

The factor tree of 12 can be represented as follows:

12

/ \

2 6

/ \

2 3

Illustrated version of this factor tree is given in the article above.

4. Is 12 a Factor of 25?

No, 12 is not a factor of 25. The factors of 25 are 1, 5, and 25 only.

5. Is 12 a Factor or Multiple of 12?

12 is both a factor and a multiple of 12. As a factor, it divides 12 exactly, and as a multiple, it is the result of multiplying 12 by 1.

6. What is Division Method of Factors of 12?

Prime factorization is also known as the division method for finding factors, as both methods involve dividing a number by various small prime numbers.