The product of a multiplication problem is 144. What do you know about the factors?

Answer 1

If the product of a multiplication problem is 144, this means that 144 has multiple factors. Factors are integers that can be multiplied together to give the product.

Here are some important points about the factors of 144:

1. Factor Pairs: The factors of 144 can be paired to multiply to 144. Some factor pairs include:

   • \(1 \times 144\)
   • \(2 \times 72\)
   • \(3 \times 48\)
   • \(4 \times 36\)
   • \(6 \times 24\)
   • \(8 \times 18\)
   • \(9 \times 16\)
   • \(12 \times 12\)

2. Total Number of Factors: To find the total number of factors, you can use the prime factorization of 144. The prime factorization is:

   • \(144 = 2^4 \times 3^2\) Using the rule that if a number is factored into \(p_1^{e_1} \times p_2^{e_2} \), the total number of factors is \((e_1 + 1)(e_2 + 1)\), the total number of factors of 144 is:
   • \((4 + 1)(2 + 1) = 5 \times 3 = 15\)

3. Divisibility: All factors of 144 will evenly divide into 144 without leaving a remainder.

4. Evenness: Since 144 is an even number, all of its factors will also retain some even properties. Specifically, it will have both even and odd factors.

5. Square Factor: 144 is a perfect square since \(12 \times 12 = 144\).

6. Positive and Negative Factors: In addition to the positive factors, each positive factor has a corresponding negative factor. So, -1, -2, -3, etc., are also factors.

In summary, the factors of 144 include: \(1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144\) (and their negatives), with a total of 15 factors overall.

Answer 2

what do I write?

Answer 3

If you're looking to summarize the information about the factors of 144, here’s a concise way to write it:

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Factors of 144:

The product of the multiplication problem is 144, which has various factors. Here are some key points:

1. Factor Pairs: The pairs of factors that multiply to give 144 include:

   • \(1 \times 144\)
   • \(2 \times 72\)
   • \(3 \times 48\)
   • \(4 \times 36\)
   • \(6 \times 24\)
   • \(8 \times 18\)
   • \(9 \times 16\)
   • \(12 \times 12\)

2. Total Number of Factors: The prime factorization of 144 is \(2^4 \times 3^2\). The total number of factors is calculated as \((4 + 1)(2 + 1) = 15\).

3. Divisibility: All factors of 144 evenly divide the number without leaving a remainder.

4. Even Factors: Since 144 is an even number, it contains both even and odd factors.

5. Perfect Square: 144 is a perfect square because it can be expressed as \(12 \times 12\).

6. Positive and Negative Factors: The factors include both positive and negative numbers. In addition to the positive factors, each has a corresponding negative factor.

List of Factors: The complete list of factors for 144 is: \[ 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 \] and their negative counterparts.

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Answer 4

I don't need to explain anything just make it simple but make sure its 100% correct.

Answer 5

Sure! Here’s a simple and accurate summary about the factors of 144:

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The factors of 144 are:

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

Each factor pairs with another to multiply to 144. For example:

• \(1 \times 144\)
• \(2 \times 72\)
• \(3 \times 48\)
• \(4 \times 36\)
• \(6 \times 24\)
• \(8 \times 18\)
• \(9 \times 16\)
• \(12 \times 12\)

144 has a total of 15 factors, and it is also a perfect square (\(12 \times 12\)).

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Answer 6

STOP REPEATING THE SAME THING OVER AND OVER

Answer 7

I apologize for any frustration caused. Here’s a concise list without repetitions:

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

Total Factors: 15
Perfect Square: Yes (12 x 12)

Let me know if you need anything else!

Answer 8

GIVE A SHORT AND PERFECT ANSWER!!!

Answer 9

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

Total factors: 15.

Perfect square: Yes (12 x 12).

Answer 10

eXPLAIN WITH WORDS HOW DO I KNOW ABOUT THE FACTORS

Answer 11

To determine the factors of a number, you can follow these steps:

1. Definition of Factors: Understand that factors are numbers that can be multiplied together to yield the original number. For example, if you say \(a\) and \(b\) are factors of \(c\), then \(a \times b = c\).

2. Start from 1: Begin by identifying the number 1, since it is a factor of every integer.

3. Check Divisibility: For each integer starting from 1, check whether it can divide the original number without leaving a remainder. For example, for 144, check if:

   • \(144 \div 1 = 144\) (valid factor)
   • \(144 \div 2 = 72\) (valid factor)
   • \(144 \div 3 = 48\) (valid factor)
   • Continue this process for each whole number up to 144.

4. Pairing Factors: Recognize that factors come in pairs. For instance, if you find that \(2\) is a factor, then \(72\) (as \(144 \div 2 = 72\)) is also a factor.

5. Identify Perfect Squares: If the number is a perfect square (like 144, which equals \(12 \times 12\)), then the middle factor will repeat.

6. List All Factors: Continue checking numbers up to the square root of the original number (which for 144 is 12). Include both the factor and its pair in your list.

7. Count: Finally, tally all the unique factors you’ve identified, ensuring you include negative factors if applicable (e.g., -1, -2, etc.).

By following these steps, you can systematically find all the factors of any number.