what times what equals 169

Guri Bee

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21-10-2024

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Unlocking the Mystery: What Times What Equals 169?

Finding the factors of a number, or the numbers that multiply together to give that number, is a fundamental concept in mathematics. Let's explore the question: what times what equals 169?

The Power of Prime Factorization

The most reliable way to find the factors of a number is through prime factorization. Prime numbers are whole numbers greater than 1 that can only be divided by 1 and themselves (examples: 2, 3, 5, 7, 11).

Here's how to prime factorize 169:

1. Divide by the smallest prime number: 169 is not divisible by 2 or 3. However, it is divisible by 13.
2. Continue dividing: 169 / 13 = 13
3. Express as prime factors: 169 = 13 x 13

Therefore, the prime factorization of 169 is 13 x 13.

Finding the Pairs

Since we have two factors of 13, we know that 13 x 13 = 169.

But remember, multiplication is commutative, meaning the order doesn't matter! We can also say 13 x 13 = 169.

Real-World Applications

Understanding factors is essential in many areas of life, such as:

• Geometry: Calculating the area of a square with a side length of 13 units.
• Algebra: Solving equations involving variables.
• Computer Science: Implementing algorithms for efficient data processing.

Beyond the Basics

While 13 x 13 is the only solution using whole numbers, there are infinitely many solutions if we include decimals. For example:

• 1.3 x 130 = 169
• 16.9 x 10 = 169

And so on! This demonstrates that there are multiple ways to represent the same product.

Let's Recap:

• The prime factorization of 169 is 13 x 13.
• 13 x 13 = 169, and vice versa.
• Understanding factors has wide-ranging applications across different fields.

Remember: Exploring the world of numbers can be a rewarding journey! So keep asking questions and digging deeper – you never know what you might discover.