Question

Write 150 as a productof as many factors as possible

Answer 1

To write 150 as a product of as many factors as possible, it is expressed as 150 = 2¹ × 3¹ × 5¹ × 5¹, which is the number broken down into its prime factors, each represented with an exponent of 1.

Step-by-step explanation:

To write the number 150 as a product of as many factors as possible, we need to do a prime factorization of the number. Prime factorization is breaking down a composite number into the set of prime numbers which, when multiplied together, give the original number. The prime factors of 150 are 2, 3, 5, 5, since 150 = 2 × 3 × 5 × 5. Now, since we want as many factors as possible, we can include the power of 1 to some of the factors (since any number to the power of 1 is itself). So the most extended product of factors for 150 we could write would be:

• 150 = 2¹ × 3¹ × 5¹ × 5¹

This expression shows 150 as a product of four factors. Remember that 5¹ is equivalent to 5, so writing the prime number with an exponent of 1 is just a formal way to express the prime factor.