If a number completely divides 144 without leaving a remainder, then that number is called a factor of 144. So we can say that the factors of 144 are the divisors of 144. Here, we will learn about the factors of 144 and the prime factors of 144.
- 144 = 2×2×2×2×3×3 = 24 × 32 is the prime factorization of 144
- Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
- Prime factors of 144: 2 and 3.
- Negative factors of 144: -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -36, -48, -72, -144
Table of Contents
What are the Factors of 144?
To find the factors of 144 by the multiplication method, let us first write the number 144 multiplicatively in all possible ways. We definitely have:
| 144 = 1×144 | 1, 144 are factors of 144 |
| 144 = 2×72 | 2, 72 are factors of 144 |
| 144 = 3×48 | 3, 48 are factors of 144 |
| 144 = 4×36 | 4, 36 are factors of 144 |
| 144 = 6×24 | 6, 24 are factors of 144 |
| 144 = 8×18 | 8, 18 are factors of 144 |
| 144 = 9×16 | 9, 16 are factors of 144 |
| 144 = 12×12 | 12 is a factor of 144 |
We observe that there are no other ways we can write 144 multiplicatively. So we will stop right now. Note that the numbers in brown color are the factors of 144.
So the factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.
We know that if m is a factor of 144 then -m is also a factor of 144. So the negative factors of 144 are -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -36, -48, -72, and -144.
Pair Factors of 144
| 144 = a×b | Factors in Pairs (a,b) |
| 144 = 1×144 | (1, 144) |
| 144 = 2×64 | (2, 64) |
| 144 = 3×48 | (3, 48) |
| 144 = 4×36 | (4, 36) |
| 144 = 6×24 | (6, 24) |
| 144 = 8×18 | (8, 18) |
| 144 = 9×16 | (9, 16) |
| 144 = 12×12 | (12, 12) |
Positive pair factors of 144: Thus the positive pair factors of 144 are (1, 144), (2, 64), (3, 48), (4, 36), (6, 24), (8, 18), (9, 16), and (12, 12).
Negative pair factors of 144: It is known that if (m, n) is a positive pair factor of 144 then (-m, -n) is a negative pair factor of 144. So all the negative pair factors of 144 are (-1, -144), (-2, -64), (-3, -48), (-4, -36), (-6, -24), (-8, -18), (-9, -16), and (-12, -12).
Number of Factors of 144
From above we have calculated the factors of 144 which are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.
Thus the total number of factors of 144 is fifteen.
Prime Factors of 144
Note that the factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144. Among these factors, we observe that only 2 and 3 are prime numbers as they do not have any proper divisors.
∴ the prime factors of 144 are 2 and 3.
Also Read:
| Factors of 48: | 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 |
| Factors of 24: | 1, 2, 3, 4, 6, 8, 12, 24 |
| Factors of 27: | 1, 3, 9, 27 |
| Factors of 32: | 1, 2, 4, 8, 16, 32 |
Question: What are the factors of 144?
Video Solution:
How to Find Factors of 144?
Now we will determine the factors of 144 by division method. In this method, we will try to find the numbers that can divide 144 with the remainder zero. See that
| 144/1=144 and the remainder is 0. | ∴ 1 and 144 are factors of 144. |
| 144/2=64 and the remainder is 0. | ∴ 2 and 64 are factors of 144. |
| 144/3=48 and the remainder is 0. | ∴ 3 and 48 are factors of 144. |
| 144/4=36 and the remainder is 0. | ∴ 4 and 36 are factors of 144. |
| 144/6=24 and the remainder is 0. | ∴ 6 and 24 are factors of 144. |
| 144/8=18 and the remainder is 0. | ∴ 8 and 18 are factors of 144. |
| 144/9=16 and the remainder is 0. | ∴ 9 and 16 are factors of 144. |
| 144/12=12 and the remainder is 0. | ∴ 12 is a factor of 144. |
Note that no numbers other than the numbers in violet color can divide 144. So the numbers in violet color, that is, 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144. are the complete list of factors of 144.
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