Prime factor of 260
Understand the Problem
The question is asking for the prime factors of the number 260. To solve this, we will find the prime numbers that multiply together to give us 260.
Answer
The prime factors of 260 are $2$, $5$, and $13$.
Answer for screen readers
The prime factors of 260 are $2$, $5$, and $13$.
Steps to Solve
- Start with the number 260
In order to find the prime factors, we begin by identifying the smallest prime number that divides 260. The smallest prime number is 2.
- Divide by 2
Perform the division of 260 by 2:
$$ 260 \div 2 = 130 $$
So, we can write:
$$ 260 = 2 \times 130 $$
- Continue factoring 130
Now, we take the result, 130, and check if it can be divided by 2 again:
$$ 130 \div 2 = 65 $$
Thus, we can express 130 as:
$$ 130 = 2 \times 65 $$
So, updating our expression:
$$ 260 = 2 \times 2 \times 65 $$
- Factor 65
Next, we need to find the prime factors of 65. The smallest prime number that works is 5:
$$ 65 \div 5 = 13 $$
This gives us:
$$ 65 = 5 \times 13 $$
- Write the final expression
Now, combining all the factors together, we have:
$$ 260 = 2 \times 2 \times 5 \times 13 $$
Which can also be expressed as:
$$ 260 = 2^2 \times 5 \times 13 $$
- Identify the prime factors
The prime factors of 260 are: 2, 5, and 13.
The prime factors of 260 are $2$, $5$, and $13$.
More Information
Prime factorization is important in various fields of mathematics, including number theory and cryptography. Every integer greater than 1 can be uniquely expressed as a product of prime numbers, and this uniqueness is fundamental in the study of numbers.
Tips
- Forgetting to check larger prime factors: Some may stop factoring too early, missing other prime factors.
- Assuming all factors are prime: Remember that not all numbers you factor are prime; confirm their primality.
