Factors of 126 Using Prime Factorization
What are the Factors of 126?
Factors of 126 are those numbers that divide 126 without leaving any remainder: in other words, we can say factors of 126 will divide it evenly.
The factors of 126 can be positive as well as negative but they cannot be decimal numbers or fractions. The quotient obtained on dividing 126 by its factor is also a factor of 126.
Factors of 126
Factors | Factor pairs | Prime factors |
|---|---|---|
1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126 | (1, 126), (2, 63), (3, 42) (6, 21), (7, 18), (9, 14) | 126 = 2 × 3 × 3 × 7 |
For example, 6 is a factor of 126 because on dividing 126 by 6 it leaves no remainder and 21 as the quotient, which is also a factor of 126.
Factor List for Number 126
Divisor | Is the number a factor of 126 ? | Multiplication Equation |
|---|---|---|
1 | Yes, 1 is a factor of every number | 1 × 126 = 126 |
2 | Yes, 126 is even | 2 × 63 = 126 |
3 | Yes, 1 + 2 + 6 = 9, 126 is divisible by 3 | 3 × 42 = 126 |
4 | No,126 ÷ 4 = 31 Remainder = 2 | - |
5 | No, 126 ÷ 5 = 25 Remainder = 1 | - |
6 | Yes, 126 is even and divisible by 3 | 6 × 21 = 126 |
7 | Yes, 126 ÷ 7 = 18 Remainder = 0 | 7 × 18 = 126 |
8 | No, 126 ÷ 8 = 15 Remainder = 6 | - |
9 | Yes, 126 ÷ 9 = 14 Remainder = 0 | 9 × 1 4 = 126 |
So the factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63 and 126.
Prime Factors of 126
A factor tree can be used to determine the prime factors of 126 as shown in the figure.
From the factor tree we can see that the prime factorization of 126 is; 2 x 3 x 3 x 7.
This means 2, 3 and 7 are the Prime factors of 126.
Factor Pairs of 126
The factor pair of any number is a set of two natural numbers which when multiplied results in the original number. So the two numbers are factors of the original number. Also not that a factor pair can be negative or positive.
[Note: Product of two negative numbers is positive.]
The factor pair of 126 is the set of two factors of 126 which when multiplied produce 126 as the result.
Thus the factor pairs of 126 can be obtained from the list of its factors.
Positive factors of 126 | Positive factor pairs of 126 |
|---|---|
1 x 126 | (1, 126) |
2 x 63 | (2, 63) |
3 x 42 | (3, 42) |
6 x 21 | (6, 21) |
7 x 18 | (7, 18) |
9 x 14 | (9, 14) |
Read More:
Rapid Recall
Solved Factors of 126 Examples
Example 1: There are 3 classes going on a field trip. The classes will use 2 buses. Can the teachers have an equal number of students in each bus?
Class | Students |
|---|---|
1 | 40 |
2 | 50 |
3 | 36 |
Solution:
Step 1:Add to find out how many students are going on the field trip.
40 + 50 + 36 = 126 [Add]
So, 126 students are going on the field trip.
Step 2: Is the total number of students divisible by the number of buses?
Since the number 126 is an even number.
So, 126 is divisible by 2 or 2 is a factor of 126.
Hence, the teachers can have an equal number of students in each bus.
Example 2: Find the common factors of 192 and 126.
Solution:
Factors of 192: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96 and 192
Factors of 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63 and 126
So, the common factors of 126 and 192 are 1, 2, 3, and 6.
Example 3: What are the common factors of 126 and 168?
Solution:
Factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126 and
Factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168.
So, the common factors of 126 and 168 are 1, 2, 3, 6, 7, 14, 21, and 42.
Yes, 7 is a factor of 126. As the number 7 divides 126 exactly and leaves no remainder, 7 is a factor of 126.
Yes, 126 is a composite number as it has factors other than 1 and itself, that is, 126. In other words the number 126 has more than two factors.
The factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63 and 126
So, the least factor of 126 is 1 and the greatest factor is 126 itself.
The factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63 and 126
Hence, the sum of the all the factors of 126 is
= 1 + 2 + 3 + 6 + 7 + 9 + 14 + 18 + 21 + 42 + 63 + 126 = 312
Hence, the sum is 312.
Factors of 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63 and 126. So there are 12 factors of 126.