Factors of 12

Factors of 12 are the list of integers that can be evenly divided into 12. There are overall 6 factors of 12 among which 12 is the biggest factor and its positive factors are 1, 2, 3, 4, 6 and 12. The sum of all factors of 12 is 28. Its Prime Factors are 1, 2, 3, 4, 6, 12 and (1, 12), (2, 6) and (3, 4) are Pair Factors.

• Factors of 12: 1, 2, 3, 4, 6 and 12
• Negative Factors of 12: -1, -2, -3, -4, -6 and -12
• Prime Factors of 12: 2, 3
• Prime Factorization of 12: 2 × 2 × 3 = 2² × 3
• Sum of Factors of 12: 28

What the Factors of 12?

A factor is a number that divides the given number without resulting in any remainder. Factors of 12 are pairs of those numbers whose products result in 12.m 3 and 4 are factors of 12, that is, 4 divides 12 into equal parts of 3 each. Similarly, we can calculate other factors of 12.

How to Calculate Factors of 12?

Let’s learn how to find factors of 12:

• Step 1: Write down the number to be factored in.
• Step 2: Find the two numbers whose product gives 12.

Let's say we take two numbers, 3 and 4. 3 is a prime number. Hence, it can be factored as 1 and the number itself.

• 4 can be written as 4 = 2 × 2
• 4 is not a prime number. Hence, it can be factorized as a product of 2 and 2, apart from the product of 1 and the number itself, that is, 4.
• Hence 4 can be factored as: 4 = 2 × 2 × 1
• Hence, 12 can be written as: 12 = 2 × 2 × 3

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

Explore factors using illustrations and interactive examples.

• Factors of 121- The factors of 121 are 1, 11, 121
• Factors of 125- The factors of 125 are 1, 5, 25, 125
• Factors of 128- The factors of 128 are 1, 2, 4, 8, 16, 32, 64, 128
• Factors of 112- The factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112
• Factors of 512 - The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512
• Factors of 20 - The factors of 1, 2, 4, 5, 10, 20

Factors of 12 by Prime Factorization

When we write a number as a product with all its factors being prime it is called prime factorization. Let's find factors of 12 using prime factorization.

• Step 1: Write the pair of factors, which on multiplication, gives the required number.
• 12 can be factored as a product of 6 and 2.
• Step 2: Check the factors whether each one of them is prime or not. 6 is not a prime number and can be dissociated as a product of 2 and 3.
• 2 is a prime number and can be dissociated as 1 and the number itself, that is, 2.
• Step 3: As per the criterion, 12 can be written as 12 = 6 × 2 = 2 × 2 × 3
• It can also be written as 12 = 2² × 3

Now that we have done the prime factorization of our number, we can multiply them and get the other factors. Can you try and find out if all the factors are covered or not?

As you might have already guessed, for prime numbers, there are no other factors.

Think Tank:

• Ms. Susan is arranging a field trip for her students to the Botanical Park. There are 12 students in all. She plans to arrange them in groups such that they are evenly distributed. What are the different combinations she can consider so that the groups are neither too small nor too large?

Factors of 12 in Pairs

Pair factors are pair of those numbers which when multiplied, give the product as the required number. Here the required number is 12. Let's try visualizing it using blocks.

Factors of 12 in pairs can be written as(Positive pair factors):

It is possible to have negative pair factors as well because the product of two negative numbers also gives a positive number.

Let's have a look at negative pair factors or factors of negative 12:

Important Notes:

• 12 is a non-perfect square number. Thus, it will have an even number of factors. This property holds true for every non-perfect square number.
• To find out if a number is a factor of 12, divide it by 3 as well as 4. If that number is divisible by both, then it's a factor of 12.
• As 12 is an even number, all of its factors will also be even.
• The negative factors of 12 are -1, -2, -3, -4, -6, -12.
• Factors are never fractions or decimals.