What is the prime factorization of 700?

To find the prime factorization of 700, we start by dividing the number by the smallest prime number, which is 2.

700 is an even number, so we can divide it by 2:

• 700 ÷ 2 = 350

Next, we take 350 and divide it by 2 again:

• 350 ÷ 2 = 175

Now, we have 175, which is not an even number. So we will check the next smallest prime number, which is 3:

• 175 is not divisible by 3, so we try the next prime, which is 5:

• 175 ÷ 5 = 35

Next, we take 35 and divide it by 5 again:

• 35 ÷ 5 = 7

Finally, we are left with 7, which is itself a prime number. Therefore, we can stop here.

In summary, the prime factorization of 700 can be expressed as:

• 2 × 2 × 5 × 5 × 7

To write this as a more compact expression, we can use exponents for the repeated factors:

• 2² × 5² × 7

So, the prime factorization of 700 is 2² × 5² × 7.