# Factors of 75 – What are the prime factors of 75 ? | Business Mathematics

## Factors of 75

In order to find the factors of a number, you can list out the numbers that divide evenly into that number. The factors of 75 are 1, 3, 5, 15, 25, and 75. The following numbers divide evenly into 75, so you can use them to determine the factors of 75:

1, 3, 5, 15, 25, 75

These are all the factors of 75.

In other words, factors are whole numbers that divide evenly into another number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, since each of these numbers divides evenly into the number 12.

• There is always a difference between a number’s factors and the number itself. For instance, the factors of 75 are all less than or equal to 75.
• The factors of 75 are 1 and 75, since every number is made up of at least two factors: firstly, it is a number, and secondly, it is itself.
• Prime numbers consist of only one factor: 1 and themselves. For example, the number 7 has only two factors: 1 and itself.
• There are several factors in the number 75, which makes it a composite number. For example, the number has one, three, five, fifteen, twenty-five, and seventy-five factors.

### How many prime factors does 75 have? A prime factorization of 75 is the product of a number’s prime factors. The prime factorization of 75 is:

75 = 3 5 5

In this expression, 3 and 5 are the prime factors of 75. 3 and 5 are both prime numbers because they have only two factors: 1 and themselves. The number 75 is a composite because it has more than two factors (1, 3, 5, 15, 25, and 75).

To find the prime factorization of a number, you can divide the number by the smallest prime factor and continue dividing by smaller prime factors until you can no longer do so. For example, to find the prime factorization of 75, you can start by dividing 75 by 3:

75 / 3 = 25

25 is not a prime number, so you can divide it by its smallest prime factor, 5:

25 / 5 = 5

5 is a prime number, so the prime factorization of 75 is 3 5 5 = 75.

### What are all multiples of 75? The multiples of 75 are the numbers that are evenly divisible by 75. To find the multiples of 75, you can start with 75 and continue adding 75 to get the next multiple. Here is a list of the first few multiples of 75:

75, 150, 225, 300, 375, 450, 525, 600, 675, 750, 825, …

The multiples of 75 are all the numbers of form 75n, where n is an integer. For example, the multiples of 75 are 75, 150, 225, 300, 375, and so on. The first few multiples of 75 are 75, 150, 225, 300, and 375.

### What is the square factor of 75? The square factor of 75 is the number that can be squared (multiplied by itself) to get 75. The square factor of 75 is 5.

75 = 5 * 5

To find the square factor of a number, you can start by finding the prime factorization of the number. For example, to find the square factor of 75, you can start by finding the prime factorization of 75:

75 = 3 5 5

The square factor of 75 is 5, because 5 is the only factor that appears twice in the prime factorization.

### What is a root of 75? The roots of a number are the numbers that, when multiplied by itself a certain number of times, result in the original number. For example, the square root of a number is the number that, when multiplied by itself, results in the original number. The square root of 75 is not a whole number, but it is approximately 8.66025.

The square root of a number can be represented using the radical symbol, which is the symbol “√”. For example, the square root of 75 can be written as √75.

The square root of a number is also known as the principal square root of the number. There are also other roots of a number, such as the cubic root, the fourth root, and so on. The nth root of a number is the number that, when multiplied by itself n times, results in the original number.

### What are the divisors of 75? The divisors of a number are the numbers that divide evenly into the number. The divisors of 75 are the numbers that divide evenly into 75. The divisors of 75 are 1, 3, 5, 15, 25, and 75.

To find the divisors of a number, you can list out the numbers that divide evenly into that number. For example, to find the divisors of 75, you can list out the numbers that divide evenly into 75:

1, 3, 5, 15, 25, 75

These are all the divisors of 75.

### What is the LCM of 75?

The least common multiple (LCM) of a set of numbers is the smallest number that is a multiple of all the numbers in the set. To find the LCM of 75, you can list out the multiples of 75 and find the smallest number that is a multiple of all the numbers in the set.

Here is a list of the first few multiples of 75:

75, 150, 225, 300, 375, 450, 525, 600, 675, 750, 825, …

The LCM of 75 is the smallest number in this list which is a multiple of all the numbers in the set. In this case, the LCM of 75 is 75, because it is the smallest multiple of 75.

The LCM of two or more numbers can also be found using the prime factorization of the numbers. To find the LCM of 75, you can first find the prime factorization of 75:

75 = 3 5 5

Then, you can find the LCM by multiplying the highest exponent of each prime factor. For example, the LCM of 75 is 3 5 5 = 75.

### What are the factors of negative 75?

The factors of a number are the numbers that divide evenly into the number. The factors of a negative number are the same as the factors of the corresponding positive number, but with a negative sign.

The factors of 75, a positive number, are 1, 3, 5, 15, 25, and 75. The factors of -75, a negative number, are the same as the factors of 75, but with a negative sign: -1, -3, -5, -15, -25, and -75.

To find the factors of a negative number, you can follow the same steps as finding the factors of a positive number. For example, to find the factors of -75, you can list out the numbers that divide evenly into -75:

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

These are all the factors of -75.

### What is the GCF of 75?

The greatest common factor (GCF) of a set of numbers is the largest number which is a factor of all the numbers in the set. To find the GCF of 75, you can list out the factors of 75 and find the largest number that is a factor of all the numbers in the set.

The factors of 75 are 1, 3, 5, 15, 25, and 75. The GCF of 75 is the largest number in this list which is a factor of all the numbers in the set. In this case, the GCF of 75 is 1, because it is the largest factor of 75 that is also a factor of all the other numbers in the set.

The GCF of two or more numbers can also be found using the prime factorization of the numbers. To find the GCF of 75, you can first find the prime factorization of 75:

75 = 3 5 5

Then, you can find the GCF by multiplying the common prime factors. For example, the GCF of 75 is 3 * 5 = 15.

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