Prime factorization of 640
Understand the Problem
The question is asking for the prime factorization of the number 640, which means we need to express 640 as a product of its prime factors.
Answer
The prime factorization of 640 is \( 2^7 \times 5^1 \).
Answer for screen readers
The prime factorization of 640 is ( 2^7 \times 5^1 ).
Steps to Solve
-
Start with the number
We begin with the number 640. -
Divide by the smallest prime number
First, we divide 640 by 2 (the smallest prime number).
$$ 640 \div 2 = 320 $$
So, we can write ( 640 = 2 \times 320 ). -
Continue dividing by 2
We continue dividing by 2:
$$ 320 \div 2 = 160 $$
Now we have ( 640 = 2 \times 2 \times 160 ). -
Keep dividing by 2
Let's divide 160 by 2 again:
$$ 160 \div 2 = 80 $$
Now we can express it as ( 640 = 2 \times 2 \times 2 \times 80 ). -
Repeat the division
Continue dividing 80 by 2:
$$ 80 \div 2 = 40 $$
This gives us ( 640 = 2 \times 2 \times 2 \times 2 \times 40 ). -
Divide 40 by 2
Now divide 40 by 2:
$$ 40 \div 2 = 20 $$
Updating our factorization: ( 640 = 2 \times 2 \times 2 \times 2 \times 2 \times 20 ). -
One more division by 2
Divide 20 by 2:
$$ 20 \div 2 = 10 $$
Now we have ( 640 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 10 ). -
Final division by 2
Lastly, divide 10 by 2:
$$ 10 \div 2 = 5 $$
We can express this as ( 640 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 5 ). -
Finishing up
Since 5 is a prime number, we conclude the factorization:
$$ 640 = 2^7 \times 5^1 $$
The prime factorization of 640 is ( 2^7 \times 5^1 ).
More Information
The number 640 can be seen in various contexts, such as in computer science as it relates to memory storage (e.g., 640 kilobytes) or in areas of number theory where factorization plays an important role in understanding the properties of numbers.
Tips
- Not recognizing that 5 is prime: Some may mistakenly try to further factor 5, when it cannot be factored further.
- Stopping too early: Ensure to keep dividing until no other prime factors are available.
