Find the Number: What Does 19 x 2 x 3 Equal?

Q: What exactly are prime factors?

Prime factors are the prime numbers that multiply together to create a composite number. Think of them as the building blocks - just like 19, 2, and 3 are the building blocks that create 114.

Q: Why do we multiply the prime factors instead of adding them?

Prime factorization shows how a number is built through multiplication. When we write $ 114 = 19 \times 2 \times 3 $, we're showing the multiplicative structure, not an additive one.

Q: Does the order of multiplication matter?

No! Thanks to the commutative property, you can multiply in any order. Whether you do $ 19 \times 2 \times 3 $ or $ 3 \times 19 \times 2 $, you'll get the same answer: 114.

Prime Factorization with Multiplication Products

What is the number whose prime factors are: $19,2,3$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the number with the given prime factors

00:03 To find the number, multiply all factors by each other

00:07 Use the commutative property and arrange for easier solving

00:12 Calculate one multiplication at a time and continue

00:18 Break down 19 into 10 plus 9, and multiply accordingly

00:23 Calculate the multiplications

00:34 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

What is the number whose prime factors are: $19,2,3$

Step-by-step solution

To solve this problem, we will follow these steps:

Step 1: Identify the given prime factors of the number, which are 19, 2, and 3.
Step 2: Multiply these prime factors to find the number.

Let's work through each step:

Step 1: The problem tells us the prime factors of the number are $19, 2,$ and $3$ .

Step 2: We will multiply these factors together to find the number:

19 \times 2 \times 3

First, multiply $19 \times 2 = 38$ .

Next, multiply the result by 3:

38 \times 3 = 114

Thus, by multiplying the given prime factors, we find that the number is $114$ .

Therefore, the solution to the problem is $114$ .

Final Answer

$114$

Key Points to Remember

Essential concepts to master this topic

Prime Factors: Individual prime numbers that multiply to form composite numbers
Technique: Multiply all prime factors: $19 \times 2 = 38$ , then $38 \times 3 = 114$
Check: Verify by dividing 114 by each prime factor completely ✓

Common Mistakes

Avoid these frequent errors

Adding prime factors instead of multiplying
Don't add the prime factors like 19 + 2 + 3 = 24! This gives a completely wrong answer because prime factorization requires multiplication, not addition. Always multiply all prime factors together to find the original number.

Practice Quiz

Test your knowledge with interactive questions

Write all the factors of the following number: $$ 6 $$

FAQ

Everything you need to know about this question

What exactly are prime factors?

Prime factors are the prime numbers that multiply together to create a composite number. Think of them as the building blocks - just like 19, 2, and 3 are the building blocks that create 114.

Why do we multiply the prime factors instead of adding them?

Prime factorization shows how a number is built through multiplication. When we write $114 = 19 \times 2 \times 3$ , we're showing the multiplicative structure, not an additive one.

Does the order of multiplication matter?

No! Thanks to the commutative property, you can multiply in any order. Whether you do $19 \times 2 \times 3$ or $3 \times 19 \times 2$ , you'll get the same answer: 114.

How can I check if my answer is correct?

Divide your answer by each prime factor one at a time. For 114: $114 \div 2 = 57$ , $57 \div 3 = 19$ , $19 \div 19 = 1$ . If you end with 1, you're correct!

What if I multiply in a different order and get a different answer?

If you get a different answer, double-check your arithmetic! The order doesn't matter mathematically, but calculation errors can happen. Try breaking it into steps: first multiply two numbers, then multiply by the third.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Division - Advanced questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime