# What are the factors and prime factors of 144?

144 is a composite number because it has factors other than 1 and itself. It is not a prime number.

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if the definition you are using excludes 1, they are 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, and 72.

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NOTE: There cannot be common factors, a greatest common factor, or a least common multiple because "common" refers to factors or multiples that two or more numbers have in common.

Here are steps showing one method to find the prime factors and prime factorization of 144.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144

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**factors**of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144. It is square number, 12^{2}, so it has an odd number of factors.The

**factor pairs**of 144 are 1 x 144, 2 x 72, 3 x 48, 4 x 36, 6 x 24, 8 x 18, 9 x 16, and 12 x 12.The

**proper factors**of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, and 72 or,if the definition you are using excludes 1, they are 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, and 72.

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**prime factors**of 144 are 2, 2, 2, 2, 3, and 3. Note: There is repetition of these factors, so if the prime factors are being listed instead of the prime factorization, usually only the distinct prime factors are listed.The 2

**distinct prime factors**(listing each prime factor only once) of 144 are 2 and 3.The

**prime factorization**of 144 is 2 x 2 x 2 x 2 x 3 x 3 or, in index form (in other words, using exponents), 2^{4}x 3^{2}.NOTE: There cannot be common factors, a greatest common factor, or a least common multiple because "common" refers to factors or multiples that two or more numbers have in common.

Here are steps showing one method to find the prime factors and prime factorization of 144.

- Factor 144
- 144 = 12 x 12
- 12 can be written as 4 x 3
- Therefore, 144 = 4 x 3 x 4 x 3
- 4 can be written as 2 x 2
- Therefore 144 = 2 x 2 x 3 x 2 x 2 x 2
- Hence, putting them in numerical order, 144 is 2 x 2 x 2 x 2 x 3 x 3
- Then you would usually write your final answer as 2
^{4}x 3^{2}

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144