Factors of 12 Using Prime Factorization
Factors of 12
What are the Factors of 12?
Integers that divide 12 without leaving any remainder are known as factors of 12.
For example, 3 is a factor of 12 because when we divide 12 by 3, the quotient is 4 and the remainder is 0. Here the quotient is also a factor of 12.
So, to check if the number is a factor of 12 or not, divide 12 by that number and verify that the remainder is zero or not.
Factor List of 12
The factors of 12 are 1, 2, 3, 4, 6, and 12.
Prime Factors of 12
The number 12 is a composite number, that is, it has more than two numbers as its factors. To find the prime factors, first we will divide the number 12 by its smallest prime factor, that is, 2.
12 ÷ 2 = 6
Again, divide by 2;
6 ÷ 2 = 3
Now, divide by the next prime number, that is, 3.
3 ÷ 3 = 1
So, the prime factorization of 12 = 2 × 2 × 3 or \( 2^2\) × 3.
This means that 2 and 3 are the prime numbers of 12.
Factor Pairs of 12
Factor pairs are two factors that when multiplied together result in the original number.
Example: (2, 6) is the factor pair of 12.
The factor pairs can be a positive pair or a negative pair.
Positive Pair Factors of 12
When two positive numbers are multiplied the product is positive.
Hence, the positive factor pairs of 12 are (1, 12), (2, 6), and (3, 4).
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Rapid Recall
Factors of 12 are;
Solved Factors of 12 Examples
Example 1: Find the common factor of 12 and 120.
Solution:
Factors of 12 = 1, 2, 3, 4, 6, and 12
Factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120
Therefore, the common factors of 12 and 120 are 1, 2, 3, 4, 6, and 12.
Example 2: Find the common factors of 12 and 17.
Solution:
Factors of 12 = 1, 2, 3, 4, 6, and 12
Factors of 17 = 1 and 17
Therefore, the common factor of 12 and 17 is 1.
Example 3: Find the common factors of 8 and 12.
Solution:
Factors of 8 = 1, 2, 4, and 8
Factors of 12 = 1, 2, 3, 4, 6, and 12
Therefore, the common factors of 8 and 12 are 1 and 2.
Example 4: There are 12 players on an athletic sports team. Can they participate in a relay race as a team of four with no player left out? If yes, then also find the number of teams that can be formed.
Solution:
To find if 12 members can be divided into groups of four, let us look at the factors of 12.
Factors of 12 are 1, 2, 3, 4, 6, and 12
As 4 is a factor of 12, we can divide the entire athletic team into groups of four and no player will be left out.
Also, the number of relay race teams that can be formed by grouping are:
= \( \frac{12}{4}\)
= 3
Therefore, there will be 3 teams formed for the relay race.
The factors of 12 are 1, 2, 3, 4, 6, and 12
So, the least factor of 12 is 1 and the greatest factor is 12 itself.
The factors of 12 are 1, 2, 3, 4, 6, and 12
Sum of factors = 1 + 2 + 3 + 4 + 6 + 12 = 28
So, the sum of factors of 12 is 28.
Yes, 6 is a factor of 12. When the number 6 divides 12, the quotient is 2 and the remainder is 0.
The prime factorization of 12 is 2 × 2 × 3 or \( 2^2\) × 3.
The positive pair factors of 12 are (1, 12), (2, 6), and (3, 4)