Factor of 42 Using Prime Factorization
What are the Factors of 42?
The factors of 42 are those integers that divide 42 without leaving any remainder. In other words, we can say that the factors of 42 will divide it exactly.
The factors of 42 can be positive as well as negative. However, the factors of 42 cannot be decimals or fractions.
For example, 6 is a factor of 42 because when we divide 42 by 6, it leaves the remainder equal to 0. Also, 7, which appears as a quotient in the above division, is a factor of 42 as well.
Factors of 42
Factors | Factor pairs | Prime factors |
|---|---|---|
1, 2, 3, 6, 7, 14, 21, and 42 | (1, 42), (2, 21),(3, 14), and (6, 7) | 42 = 2 x 3 x 7 |
Factor list for the Number 42
Divisor | Is the number a factor of 42? | Multiplication Equation |
|---|---|---|
1 | Yes, 1 is a factor of every number | 1 × 42 = 42 |
2 | Yes, 42 is even. | 2 × 21 = 42 |
3 | Yes, 42 is divisible by 3 | 3 × 14 = 42 |
6 | Yes, 42 ÷ 6 = 7 Remainder = 0 | 6 × 7 = 42 |
7 | Yes, 42 ÷ 7 = 6 Remainder = 0 | 7 × 6 = 42 |
14 | Yes, 42 ÷ 14 = 3 Remainder = 0 | 14 × 3 = 42 |
21 | Yes, 42 ÷ 21 = 2 Remainder = 0 | 21 × 2 = 42 |
42 | Yes, a number is a factor of itself. | 42 × 1 = 42 |
Explaining the Prime Factors of a 42
A factor tree is used to learn about the prime factorization of 42, as shown below.
From the factor tree, we can see the prime factorization of 42 is 2 × 3 × 7.
This means that 2, 3, and 7 are the prime factors of 42.
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Factor Pairs of 42
The factor pair of 42 is the combination of two factors of 42, which when multiplied together, give 42 as the result.
The factors of 42: 1, 2, 3, 6, 7, 21, and 42.
All the combinations of two factors multiplied together to give a result of 42 are known as the factor pairs of 42.
Positive factors of 42 | Positive pair factors of 42 |
|---|---|
1 x 42 | (1, 42) |
2 x 21 | (2, 21) |
3 x 14 | (3, 14) |
6 x 7 | (6, 7) |
Rapid Recall
Solved Examples
Example 1: Find the common factors of 10 and 42.
Solution:
The factors of 42: 1, 2, 3, 6, 7, 14, 21, and 42.
The factors of 10: 1, 2, 5, and 10.
So, the common factors of 10 and 42 are 1 and 2.
Hence, 10 and 42 have two common factors.
Example 2: What are the common factors of 42 and 18?
Solution:
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42, and
The factors of 18 are 1, 2, 3, 6, 9, and 18.
So, the common factors of 42 and 18 are 1, 2, 3, and 6.
Example 3: Nancy baked 42 cookies with her mom. She wants to decide the best way to divide the cookies in rows and columns, to make them look attractive. Help Nancy find the best way to arrange the cookies.
Solution:
Factor pairs of 42 would give us ways to divide the cookies in rows and columns equally.
Factor pairs of 42 are:
1 x 42 = 42
2 x 21 = 42
3 x 14 = 42
6 x 7 = 42
Clearly, 42 cookies would look best when arranged in 6 rows and 7 columns.
Hence, factor pairs of 42 are (1, 42), (2, 21), (3, 14), and (6, 7).
No, 9 is not a factor of 42 as the number 9 does not divide 42 exactly. It leaves the remainder 6. So, 9 is not a factor of 42.
Yes, 42 is a composite number as it has factors other than one and itself. It has the factors 2, 3, 6, 7, 14, and 21 other than 1 and 42.
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.
So, the least factor of 42 is 1, and the greatest factor is 42 itself.
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.
Hence, the sum of all the factors of 42 is
= 1 + 2 + 3 + 6 + 7 + 14 + 21 + 42
= 96
Hence, the sum is 96.
Factors of 42: 1, 2, 3, 6, 7, 21, and 42.
So, there are 8 factors of 42.