The number 75 can be factored into its prime factors, which are the prime numbers that multiply together to give the original number. Let’s find the prime factorization of 75:

To begin, we check if 75 is divisible by 2. Since 75 is an odd number, it is not divisible by 2.

Next, we check if 75 is divisible by 3. The sum of the digits of 75 (7 + 5) is 12, which is divisible by 3. Therefore, 75 is divisible by 3.

Dividing 75 by 3, we get 25.

Now, let’s check if 25 is divisible by 3. The sum of its digits (2 + 5) is 7, which is not divisible by 3.

Next, we check if 25 is divisible by 5. Since 25 ends with a 5, it is divisible by 5.

Dividing 25 by 5, we get 5.

Now, let’s check if 5 is divisible by 5. It is divisible by 5.

Dividing 5 by 5, we get 1.

Putting it all together, we have:

75 = 3 × 5 × 5

So, the prime factorization of 75 is 3 × 5 × 5.

The introduction factors of 75 are 3 and 5.

## How many Factors of 75

To find the number of factors of 75, we can use its prime factorization, which is 3 × 5 × 5.

To determine the number of factors, we consider the exponents of the prime factors. In this case, we have a factor of 3 raised to the power of 1 (3^1) and two factors of 5 raised to the power of 1 (5^1 × 5^1).

To calculate the total number of factors, we add 1 to each exponent and multiply them together:

(1 + 1) × (1 + 1) = 2 × 2 = 4

Therefore, there are 4 factors of 75. These factors are: 1, 3, 5, and 75.

#### Factor Pairs of 75

To find the factor pairs of 75, we need to determine all the pairs of numbers that multiply together to give 75. Here are the factor pairs of 75:

1 × 75 = 75

3 × 25 = 75

5 × 15 = 75

-1 × -75 = 75

-3 × -25 = 75

-5 × -15 = 75

So, the factor pairs of 75 are: (1, 75), (3, 25), (5, 15), (-1, -75), (-3, -25), and (-5, -15).

#### All Factors of using Multiplication 75

To find all the factors of 75 using multiplication, we can start by listing the numbers that divide evenly into 75. We’ll include both positive and negative factors.

The factors of 75 obtained through multiplication are:

1, -1, 3, -3, 5, -5, 15, -15, 25, -25, 75, and -75.

These numbers, when multiplied by each other, will result in 75.