# Factors of 1575

Factors of 1575 are 1, 3, 5, 7, 9, 15, 21, 25, 35, 45, 63, 75, 105, 175, 225, 315, 525, and 1575

#### How to find factors of a number

 1.   Find factors of 1575 using Division Method 2.   Find factors of 1575 using Prime Factorization 3.   Find factors of 1575 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 1575

• Divide 1575 by 1: 1575 ÷ 1 : Remainder = 0
• Divide 1575 by 3: 1575 ÷ 3 : Remainder = 0
• Divide 1575 by 5: 1575 ÷ 5 : Remainder = 0
• Divide 1575 by 7: 1575 ÷ 7 : Remainder = 0
• Divide 1575 by 9: 1575 ÷ 9 : Remainder = 0
• Divide 1575 by 15: 1575 ÷ 15 : Remainder = 0
• Divide 1575 by 21: 1575 ÷ 21 : Remainder = 0
• Divide 1575 by 25: 1575 ÷ 25 : Remainder = 0
• Divide 1575 by 35: 1575 ÷ 35 : Remainder = 0
• Divide 1575 by 45: 1575 ÷ 45 : Remainder = 0
• Divide 1575 by 63: 1575 ÷ 63 : Remainder = 0
• Divide 1575 by 75: 1575 ÷ 75 : Remainder = 0
• Divide 1575 by 105: 1575 ÷ 105 : Remainder = 0
• Divide 1575 by 175: 1575 ÷ 175 : Remainder = 0
• Divide 1575 by 225: 1575 ÷ 225 : Remainder = 0
• Divide 1575 by 315: 1575 ÷ 315 : Remainder = 0
• Divide 1575 by 525: 1575 ÷ 525 : Remainder = 0
• Divide 1575 by 1575: 1575 ÷ 1575 : Remainder = 0

Hence, Factors of 1575 are 1, 3, 5, 7, 9, 15, 21, 25, 35, 45, 63, 75, 105, 175, 225, 315, 525, and 1575

#### 2. Steps to find factors of 1575 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 1575 using the division method, follow these steps:

• Step 1. Start dividing 1575 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 1575, which is 3. Divide 1575 by 3 to obtain the quotient (525).
1575 ÷ 3 = 525
• Step 3. Repeat step 1 with the obtained quotient (525).
525 ÷ 3 = 175
175 ÷ 5 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1

So, the prime factorization of 1575 is, 1575 = 3 x 3 x 5 x 5 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1575 as shown below:

So, the prime factorization of 1575 is, 1575 = 3 x 3 x 5 x 5 x 7.

#### 3. Find factors of 1575 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 1575 would be the two numbers which, when multiplied, give 1575 as the result.

The following table represents the calculation of factors of 1575 in pairs:

Factor Pair Pair Factorization
1 and 1575 1 x 1575 = 1575
3 and 525 3 x 525 = 1575
5 and 315 5 x 315 = 1575
7 and 225 7 x 225 = 1575
9 and 175 9 x 175 = 1575
15 and 105 15 x 105 = 1575
21 and 75 21 x 75 = 1575
25 and 63 25 x 63 = 1575
35 and 45 35 x 45 = 1575

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 1575. They are called negative pair factors.

Hence, the negative pairs of 1575 would be ( -1 , -1575 ) , ( -3 , -525 ) , ( -5 , -315 ) , ( -7 , -225 ) , ( -9 , -175 ) , ( -15 , -105 ) , ( -21 , -75 ) , ( -25 , -63 ) and ( -35 , -45 ) .

#### What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Every number is a factor of zero (0), since 1575 x 0 = 0.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 3, 5, 7, 9, 15, 21, 25, 35, 45, 63, 75, 105, 175, 225, 315, 525, 1575 are exact divisors of 1575.
• Factors of 1575 are 1, 3, 5, 7, 9, 15, 21, 25, 35, 45, 63, 75, 105, 175, 225, 315, 525, 1575. Each factor divides 1575 without leaving a remainder.

• Which is the smallest prime factor of 1575?

Smallest prime factor of 1575 is 3.

• Is 1575 a perfect square?

No 1575 is not a perfect square.

• What are five multiples of 1575?

First five multiples of 1575 are 3150, 4725, 6300, 7875, 9450.

• What is prime factorization of 1575?

Prime factorization of 1575 is 3 x 3 x 5 x 5 x 7.

• What are factors of 1575?

Factors of 1575 are 1, 3, 5, 7, 9, 15, 21, 25, 35, 45, 63, 75, 105, 175, 225, 315, 525, 1575.

• How do you find factors of a negative number? ( eg. -1575 )?

Factors of -1575 are -1, -3, -5, -7, -9, -15, -21, -25, -35, -45, -63, -75, -105, -175, -225, -315, -525, -1575.

• Is 1575 a whole number?

Yes 1575 is a whole number.

• Which is greatest factor of 1575?

The greatest factor of 1575 is 525.

• What are the prime factors of 1575?

The factors of 1575 are 1, 3, 5, 7, 9, 15, 21, 25, 35, 45, 63, 75, 105, 175, 225, 315, 525, 1575.
Prime factors of 1575 are 3, 3, 5, 5, 7.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 1575. Can you help her?

Prime factors of 1575 are 3, 3, 5, 5, 7.
Hence, the product of prime factors of 105.

Can you help Rubel to find out the product of the even factors of 1575?

Factors of 1575 are 1, 3, 5, 7, 9, 15, 21, 25, 35, 45, 63, 75, 105, 175, 225, 315, 525, 1575.
Even factors of 1575 are 0.
Hence, product of even factors of 1575 is; 0 = 0.

Joy wants to calculate mean of all the factors of 1575. Help him in finding the mean of 1575.

Factors of 1575 are 1, 3, 5, 7, 9, 15, 21, 25, 35, 45, 63, 75, 105, 175, 225, 315, 525, 1575.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 1575 is 1 + 3 + 5 + 7 + 9 + 15 + 21 + 25 + 35 + 45 + 63 + 75 + 105 + 175 + 225 + 315 + 525 + 1575 = 3224.
Hence, the mean of factors of 1575 is 3224 ÷ 18 = 179.11.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 1575? Help her in writing all the factors.

Positive factors are 1, 3, 5, 7, 9, 15, 21, 25, 35, 45, 63, 75, 105, 175, 225, 315, 525, 1575.
Negative factors are -1, -3, -5, -7, -9, -15, -21, -25, -35, -45, -63, -75, -105, -175, -225, -315, -525, -1575.

How many factors are there for 1575?

Factors of 1575 are 1, 3, 5, 7, 9, 15, 21, 25, 35, 45, 63, 75, 105, 175, 225, 315, 525, 1575.
So there are in total 18 factors.

Joey wants to write all the prime factors of 1575 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1575 are 3, 3, 5, 5, 7.
So in exponential form it can be written as 32 x 52 x 7.

Kevin has been asked to write 17 factor(s) of 1575. Can you predict the answer?

17 factor(s) of 1575 are 1, 3, 5, 7, 9, 15, 21, 25, 35, 45, 63, 75, 105, 175, 225, 315, 525.