Find the prime factorization of 196, using exponents when repeated factors appear
196
= 2*98
= 2*2*49
= 2*2*7*7
= 2^2 * 7^2
I am really have a hard time I need help. Prime factorization of 343
To find the prime factorization of a number, we need to express it as a product of prime numbers. Let's start by dividing 196 by the smallest prime number, 2:
196 ÷ 2 = 98
98 is still an even number, so we can divide it by 2 again:
98 ÷ 2 = 49
Now we have 49, which is a square number. Let's find its square root:
√49 = 7
Since 49 is a perfect square, we know that 7 is a prime factor of 196. Now, let's divide 196 by 7:
196 ÷ 7 = 28
Now we have 28, which is an even number. Let's divide it by 2 again:
28 ÷ 2 = 14
14 is also an even number, so we can divide it by 2 again:
14 ÷ 2 = 7
Since we have reached a factor of 7 again, we know that 7 is another prime factor of 196.
Therefore, the prime factorization of 196 is 2^2 × 7^2, where "^" denotes exponentiation.