When we talk about the prime factors of a number, we are essentially looking for all the prime numbers that can be multiplied together to give the original number. In this case, we will be exploring the prime factors of the number 700.
What is a Prime Factor?
Before we dive into finding the prime factors of 700, let’s first understand what a prime factor is. A prime factor is a prime number that can only be divided by 1 and itself without leaving a remainder. Prime numbers are numbers that have exactly two factors: 1 and the number itself.
Finding the Prime Factors of 700
To find the prime factors of 700, we will start by dividing the number by the smallest prime number, which is 2. We will continue dividing by primes until we no longer get a whole number result. Let’s break it down step by step:
- Step 1: Start by dividing 700 by the smallest prime number, which is 2.
- 700 ÷ 2 = 350
- Step 2: Next, continue dividing the result (350) by 2:
- 350 ÷ 2 = 175
- Step 3: Repeat the process with the next smallest prime number, which is 3:
- 175 ÷ 3 = 58.33 (not a whole number)
- Step 4: Move on to the next prime number, which is 5:
- 175 ÷ 5 = 35
- Step 5: Continuing with 5:
- 35 ÷ 5 = 7
- Step 6: Lastly, 7 is a prime number, and dividing 7 by 7 gives us 1.
- 7 ÷ 7 = 1
After following these steps, we have successfully found all the prime factors of 700. Now, let’s list them out:
Prime Factors of 700:
- 2
- 2
- 5
- 5
- 7
These prime factors can be multiplied together to get the original number 700:
2 x 2 x 5 x 5 x 7 = 700
Key Points to Remember
- Prime factors are prime numbers that can be multiplied together to get the original number.
- Always start with the smallest prime number and continue dividing until you reach 1.
- Prime numbers have exactly two factors: 1 and the number itself.
Conclusion
Finding the prime factors of a number like 700 can be a simple yet essential exercise in understanding the building blocks of a number. By breaking down a number into its prime factors, we gain insight into its factors and properties. Remember to follow the steps outlined above and practice finding prime factors of different numbers to strengthen your understanding of prime factorization.
