What are two different factor trees for 60?

To represent the number 60 as a product of its prime factors, we can create factor trees. Here are two different factor trees for the number 60:

Factor Tree 1:

• Start with 60.
• 60 can be divided by 2 (which is a prime number) to get 30.
• From 30, we can again divide by 2 to get 15.
• 15 can be divided by 3 (another prime number) to get 5.
• Now, 5 is a prime number itself.

Thus, the first factorization looks like this: 60 = 2 x 2 x 3 x 5, or in exponential form, 60 = 2² x 3 x 5.

Factor Tree 2:

• Again, start with 60.
• This time, we can divide 60 by 3 (which is prime) to get 20.
• From 20, divide by 2 to get 10.
• 10 can then be divided by 2 to get 5.
• 5, as mentioned before, is prime.

So, the second factorization looks like this: 60 = 3 x 2 x 2 x 5, or in exponential form, 60 = 3 x 2² x 5.

In summary, both trees confirm that the prime factorization of 60 is made up of the same prime numbers, just arranged differently: 60 = 2² x 3 x 5 and 60 = 3 x 2² x 5.