Factors of 144 | Prime Factorization of 144 | Factor Tree of 144

Factors of a given number are the numbers that can divide that number wholly with zero as the remainder and no decimal points in the quotient. A number does not just have positive pair factors but also negative pair factors. This article will help you in understanding the factors of 144 and the various methods of factorization.

What Are the Factors of 144?

The factors of 144 are the numbers that can divide the number 144 completely without any decimal number in the quotient. The factors of the number 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.

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

Negative Factors of 144: -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -36, -48, -72 and -144

Prime Factorization of 144: 2 x 2 x 2 x 2 x 3 x 3

Pair Factors of 144: (1, 144), (2, 72), (3, 48), (4, 36), (6, 24), (8, 18), (9, 16), and (12, 12).

Prime Factors of 144: 2 and 3

Sum of Factors of 144: 403

Sum of Prime Factors of 144: 5

What Are the Factors of 144 in Pairs?

There exist both negative and positive pair factors for 144, which when multiplied together produces the number 144.

Positive Pair Factors of 144

The positive pair factors of 144 are (1, 144), (2, 72), (3, 48), (4, 36), (6, 24), (8, 18), (9, 16), and (12, 12).

Negative Pair Factors of 144

The negative pair factors of 144 are (-1, -144), (-2, -72), (-3, -48), (-4, -36), (-6, -24), (-8, -18), (-9, -16), and (-12, -12).

What Is the Prime Factorization Method of 144?

The prime factors of the number 144 can be found by using the number 144. The following are the steps that are involved in that process:

• Step 1: Keep the number 144 at the top and divide it by the smallest number, which is 2.
  144 ÷ 2 = 72
• Step 2: Now, divide the number 72 by the smallest prime number and it is again 2.
  72 ÷ 2 = 36
• Step 3: Here, again the smallest number that can divide by the number 36 is 2.
  36 ÷ 2 = 18
• Step 4: The number 2 again stands to be the smallest number that can divide the number 18.
  18 ÷ 2 = 9
• Step 5: Here, the number 18 is divisible by the prime number 3.
  9 ÷ 3 = 3
• Step 6: The number 3 is divisible by the number 3.
  3 ÷ 3 = 1
• Step 7: Now the obtained number is 1. Therefore, the prime factors of 144 are 2 x 2 x 2 x 2 x 3 x 3 or else just the numbers 2 and 3.

The below image shows the prime factorization of 144.

How to Find Factors of 144 Through Division Method?

In the division method, the factors of a number are found by dividing the given number by 1 and followed by other prime numbers that can divide the given number till the remainder becomes zero and also with no decimal points in the quotient. The division method of 144 is given below:

• 144 ÷ 1 = 144
• 144 ÷ 2 = 72
• 144 ÷ 3 = 48
• 144 ÷ 4 = 36
• 144 ÷ 6 = 24
• 144 ÷ 8 = 18
• 144 ÷ 9 = 16
• 144 ÷12 = 12
• 144 ÷ 16 = 9
• 144 ÷ 18 = 8
• 144 ÷ 24 = 6
• 144 ÷36 = 4
• 144 ÷ 48 = 3
• 144 ÷ 72 = 2
• 144 ÷ 144 = 1

Therefore, the factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.

What Is the Factor Tree of 144?

The factor tree is a diagrammatic way to represent the factors of a given number. The steps involved in the process of making a factor tree of 144 are given below:

• Step 1: Keep the number 144 at the top of the factor tree and place the first set of pair factors on its branches which are 2 and 72.
• Step 2: Now place the pair factors of 72 on its branches. Those numbers are 2 and 36.
• Step 3: Again here, the number 36 has 2 and 18 as its pair factors. And so place them in the branches of 36.
• Step 4: Now place the pair factors of 18 in its branches and those numbers are 3 and 9.
• Step 5: And here, the pair factor of 9 is 3 x 3. So place it on the branches of 9 in the factor tree.
• Step 6: Now the final number is 3, which is a prime number and so we cant further add the branches to that number.

Therefore, the factors of 144 are 2 x 2 x 2 x 2 x 3 x 3. The image given below is the factor tree of 144.

Solved Examples

What are the factors of 144?
The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.

What are the pair factors of 144?
The pair factors of 144 are (1, 144), (2, 72), (3, 48), (4, 36), (6, 24), (8, 18), (9, 16), and (12, 12).

What is the sum of the factors of 144?
The sum of the factors of 144 is 403.

What are the prime factors of 144?
The prime factors of 144 are 2 and 3.

Frequently Asked Questions

What are multiples of 144?
The multiples of 144 are 144, 288, 432, 576, 720, 864, 1008, 1152, 1296, and 1440.

Is 144 a perfect square?
Yes, 144 is a perfect square and its square root is 144.

Is 144 a prime number?
No, 144 is not a prime number as it has more than two numbers as its factors. The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.

What is the cube of 144?
The cube of 144 is  2,985,984.

Why is 144 a multiple of 9?
Yes, 144 is a multiple of 9. As 9 x 16 = 144.