what times what equals 90

Daniel Parker

2 min read

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01-03-2025

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The question "What times what equals 90?" is a simple yet fundamental math problem. It's asking you to find the factors of 90 – the numbers that, when multiplied together, result in 90. There are several possible answers, depending on whether you're looking for whole numbers, integers, or even including decimals and fractions. Let's explore them.

Whole Number Factors of 90

Let's start with the most straightforward approach: finding pairs of whole numbers that multiply to 90. Here are some possibilities:

• 1 x 90: This is the most obvious pair.
• 2 x 45: Two times forty-five equals ninety.
• 3 x 30: Three multiplied by thirty gives you ninety.
• 5 x 18: Five times eighteen is also ninety.
• 6 x 15: Six multiplied by fifteen equals ninety.
• 9 x 10: Nine times ten equals ninety.

These are all the whole number pairs that multiply to 90. Notice that the pairs are essentially mirror images of each other (except for 9 x 10, which is a symmetrical pair).

Beyond Whole Numbers: Integers and Beyond

If we expand our search beyond positive whole numbers, we can include negative numbers. Since a negative number multiplied by a negative number yields a positive number, we also have these pairs:

• -1 x -90
• -2 x -45
• -3 x -30
• -5 x -18
• -6 x -15
• -9 x -10

Remember, any number multiplied by its negative counterpart will always equal a positive number.

Fractional and Decimal Factors

The possibilities become infinite when we consider fractions and decimals. For example:

• 0.5 x 180
• 0.1 x 900
• 1.5 x 60

And so on. You could find an infinite number of decimal pairs that multiply to 90.

Finding Factors: A Systematic Approach

To find all the factors of a number like 90, you can use a systematic approach:

1. Start with 1: Every number is divisible by 1.
2. Check for divisibility by prime numbers: Test if the number is divisible by 2, 3, 5, 7, and so on (prime numbers are numbers only divisible by 1 and themselves).
3. Continue until you reach the square root: Once you find a factor larger than the square root of the number (√90 ≈ 9.49), you've found all the factors.

This method ensures that you identify all the whole number factors.

Conclusion: Multiple Answers to a Simple Question

The simple question "What times what equals 90?" has multiple answers. The number of solutions depends on whether you are considering only positive whole numbers, or whether you expand to include negative numbers, fractions, or decimals. Understanding how to find the factors of a number is a fundamental skill in mathematics.