Factors of 48 can be defined into two numbers which, when multiplied together in pairs is the original number 48; alternatively, we can say that any numbers that divide 48 with zero as their remainder and leave no remainders as factors of 48. They can be either positive or negative numbers; for example (1 + 48 = 48), (1 -48 = -48), multiplying pair of negative factors will give 48 (if we multiply pair -1+-48 yields 48 as a result. We will learn the prime factorisation method with many solved examples and solved examples on factors of 48, as the prime factorization method has plenty of solved examples!
What Are the Factors of 48?
The factors of 48 are defined as any numbers that divide 48 exactly, without leaving any remainder, without multiplying in pairs resulting in an original number. Even the composite number 48 has many other factors than just 1 and 48 that constitute its factors: 1, 2, 3, 4, 6 8 12 16 24 and 48 are just some examples.
| Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48. Prime Factorization of 48: 2×2×2×2×3 or 24 × 3. |
Pair Factors of 48
Pair factors of 48 are numbers where two numbers multiplied together result in 48 as the resultant result. As previously discussed, these can either be positive or negative numbers and therefore below are both sets of positive and negative pair factors for 48:
Positive Pair Factors of 48:
| Positive Factors of 48 | Positive Pair Factors of 48 |
| 1 × 48 | (1, 48) |
| 2 × 24 | (2, 24) |
| 3 × 16 | (3, 16) |
| 4 × 12 | (4, 12) |
| 6 × 8 | (6, 8) |
Negative Pair Factors of 48:
| Negative Factors of 48 | Negative Pair Factors of 48 |
| -1 × -48 | (-1, -48) |
| -2 × -24 | (-2, -24) |
| -3 × -16 | (-3, -16) |
| -4 × -12 | (-4, -12) |
| -6 × -8 | (-6, -8) |
Factors of 48 by Division Method
To use this method to discover its factors, divide 48 into various consecutive integers until any one divides 48 exactly and leaves no remainder 0. If so, these integers become factors of 48. Now let us discuss how to find them using divisio
- Start with the number 48.
- Divide 48 by 2: 48÷2=2448÷2=24. So, 2 is a factor of 48.
- Now, divide 24 by 2: 24÷2=1224÷2=12. 2 is a factor again.
- Divide 12 by 2: 12÷2=612÷2=6. 2 is a factor once more.
- Divide 6 by 2: 6÷2=36÷2=3. 2 is not a factor anymore.
- Divide 3 by 3: 3÷3=13÷3=1. 3 is a factor.
Prime Factorisation of 48
48 is a composite number. Let us now find its prime factorization.
To find the prime factorisation of 48, we can start dividing the number by the smallest prime number , that is 2.
- 48/22 equals 24.
- 24/22 equals 12.
- 12/22 equals 6.
- 6/22 equals 3.
Now, 3 is a prime number itself. So, the prime factorization of 48 is:
48=24×31
This means that 48 can be expressed as the product of 2 raised to the power of 4 and 3 raised to the power of 1.
