Factors of 6 Using Prime Factorization
What are the Factors of 6?
The integers that can divide a number evenly are known as the factors of that number. When 6 is divided by its factor, the remainder is zero, and the quotient is also a factor of 6.
Factor List of the Number 6
6 is a composite number, that is, it has more than two factors. The factors of 6 can be obtained using divisibility rules and division facts.
Therefore, the factors of 6 are 1, 2, 3, and 6.
The Prime Factors of a Number
The factor tree below depicts the prime factors of the number 6.
Hence, the prime factorization of 6 = 2 x 3
= \(2^1~\times~3^1\)
Therefore, 2 and 3 are the prime factors of 6.
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The Positive Factor Pairs of 6
Each factor pair of 6 is a set of two positive or negative numbers, such that their product is 6. Below is a list of positive factor pairs of 6.
So the positive factor pairs of 6 are (1, 6) and (2, 3).
Solved Factors of 6 Examples
Example 1: Find the common factors of 6 and 36.
Solution:
The factors of 6 are 1, 2, 3, and 6.
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
Hence, the common factors of 6 and 36 are 1, 2, 3, and 6.
Example 2: Find the common factors of 6 and 4.
Solution:
The factors of 6 are 1, 2, 3, and 6.
The factors of 4 are 1, 2, and 4.
Hence, the common factors of 6 and 4 are 1 and 2.
Example 3: Find the common factors of 6 and 12. Callie has 6 dolls and Sheila has 12 dolls. How many groups of dolls can Callie and Sheila make together such that they have an equal number of dolls in each group?
Solution:
To find the number of groups, we need to find the common factors of 6 and 12.
The factors of 6 are 1, 2, 3, and 6.
The factors of 12 are 1, 2, 3, 4, 6, and 12.
Hence, the common factors of 6 and 12 are 1, 2, 3, and 6.
Example 4: Find the common factors of 6 and 18.
Solution:
The factors of 6 are 1, 2, 3, and 6.
The factors of 18 are 1, 2, 3, 6, 9, and 18.
Hence, the common factors of 6 and 18 are 1, 2, 3, and 6.
Therefore, there can be four groups of dolls that Callie and Sheila can form such that there are an equal number of dolls in each group. They can group them as:
1 doll in each group, or
2 dolls in each group, or
3 dolls in each group, or
6 dolls in each group.
1, 2, 3, and 6 are the factors of 6.
2 × 3 or \(2^1~\times~3^1\) is the prime factorization of 6.
(1, 6) and (2, 3) are the positive pair factors of 6.
Yes, 3 is a factor of 6. 3 divides 6 exactly and leaves the remainder 0, hence 3 is a factor of 6.
The number 6 has a total of four factors: 1, 2, 3, and 6.