Decode the Number: Prime Factors of 7, 11, and 2

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

Prime factorization means the number is the product of its prime factors. Think of it like $ 154 = 7 \times 11 \times 2 $, not $ 7 + 11 + 2 $. The multiplication represents how the number was originally built.

Q: Are 7, 11, and 2 really all prime numbers?

Yes! A prime number has exactly two factors: 1 and itself. Check: 7 = 1 × 7, 11 = 1 × 11, 2 = 1 × 2. None can be broken down further!

Prime Factorization with Product Reconstruction

What is the number whose prime factors are: $7,11,2$

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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 Find the number with the given prime factors

00:07 Calculate one multiplication at a time and continue

00:13 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: $7,11,2$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the given prime factors: $7, 11,$ and $2$ .
Step 2: Multiply these prime factors together to find the number.

Now, let's work through each step:

Step 1: The given prime factors are $7, 11,$ and $2$ .

Step 2: Multiply the factors together:
First, calculate $7 \times 11 = 77$ .
Then, multiply the result by 2: $77 \times 2 = 154$ .

Therefore, the solution to the problem is $154$ .

Final Answer

$154$

Key Points to Remember

Essential concepts to master this topic

Definition: Prime factors are the unique primes that multiply to form a number
Method: Multiply all prime factors: $7 \times 11 \times 2 = 154$
Verify: Check that 154 ÷ 7 = 22, 22 ÷ 11 = 2, 2 ÷ 2 = 1 ✓

Common Mistakes

Avoid these frequent errors

Adding prime factors instead of multiplying
Don't add the factors 7 + 11 + 2 = 20! This gives a completely different number that doesn't have the correct prime factorization. Always multiply prime factors together to reconstruct 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

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

Prime factorization means the number is the product of its prime factors. Think of it like $154 = 7 \times 11 \times 2$ , not $7 + 11 + 2$ . The multiplication represents how the number was originally built.

What if the prime factors are given in a different order?

Order doesn't matter in multiplication! Whether you calculate $7 \times 11 \times 2$ or $2 \times 7 \times 11$ , you'll get the same answer: 154.

How can I check if my answer is correct?

Divide your answer by each prime factor repeatedly. For 154: $154 ÷ 7 = 22$ , then $22 ÷ 11 = 2$ , then $2 ÷ 2 = 1$ . If you end with 1, you're correct!

What if a prime factor appears more than once?

Include it multiple times in your multiplication! For example, if the prime factors are 2, 2, 3, then the number is $2 \times 2 \times 3 = 12$ .

Are 7, 11, and 2 really all prime numbers?

Yes! A prime number has exactly two factors: 1 and itself. Check: 7 = 1 × 7, 11 = 1 × 11, 2 = 1 × 2. None can be broken down further!

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