# Factors of 4725

Factors of 4725 are 1, 3, 5, 7, 9, 15, 21, 25, 27, 35, 45, 63, 75, 105, 135, 175, 189, 225, 315, 525, 675, 945, 1575, and 4725

#### How to find factors of a number

 1.   Find factors of 4725 using Division Method 2.   Find factors of 4725 using Prime Factorization 3.   Find factors of 4725 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 4725

• Divide 4725 by 1: 4725 ÷ 1 : Remainder = 0
• Divide 4725 by 3: 4725 ÷ 3 : Remainder = 0
• Divide 4725 by 5: 4725 ÷ 5 : Remainder = 0
• Divide 4725 by 7: 4725 ÷ 7 : Remainder = 0
• Divide 4725 by 9: 4725 ÷ 9 : Remainder = 0
• Divide 4725 by 15: 4725 ÷ 15 : Remainder = 0
• Divide 4725 by 21: 4725 ÷ 21 : Remainder = 0
• Divide 4725 by 25: 4725 ÷ 25 : Remainder = 0
• Divide 4725 by 27: 4725 ÷ 27 : Remainder = 0
• Divide 4725 by 35: 4725 ÷ 35 : Remainder = 0
• Divide 4725 by 45: 4725 ÷ 45 : Remainder = 0
• Divide 4725 by 63: 4725 ÷ 63 : Remainder = 0
• Divide 4725 by 75: 4725 ÷ 75 : Remainder = 0
• Divide 4725 by 105: 4725 ÷ 105 : Remainder = 0
• Divide 4725 by 135: 4725 ÷ 135 : Remainder = 0
• Divide 4725 by 175: 4725 ÷ 175 : Remainder = 0
• Divide 4725 by 189: 4725 ÷ 189 : Remainder = 0
• Divide 4725 by 225: 4725 ÷ 225 : Remainder = 0
• Divide 4725 by 315: 4725 ÷ 315 : Remainder = 0
• Divide 4725 by 525: 4725 ÷ 525 : Remainder = 0
• Divide 4725 by 675: 4725 ÷ 675 : Remainder = 0
• Divide 4725 by 945: 4725 ÷ 945 : Remainder = 0
• Divide 4725 by 1575: 4725 ÷ 1575 : Remainder = 0
• Divide 4725 by 4725: 4725 ÷ 4725 : Remainder = 0

Hence, Factors of 4725 are 1, 3, 5, 7, 9, 15, 21, 25, 27, 35, 45, 63, 75, 105, 135, 175, 189, 225, 315, 525, 675, 945, 1575, and 4725

#### 2. Steps to find factors of 4725 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 4725 using the division method, follow these steps:

• Step 1. Start dividing 4725 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 4725, which is 3. Divide 4725 by 3 to obtain the quotient (1575).
4725 ÷ 3 = 1575
• Step 3. Repeat step 1 with the obtained quotient (1575).
1575 ÷ 3 = 525
525 ÷ 3 = 175
175 ÷ 5 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1

So, the prime factorization of 4725 is, 4725 = 3 x 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 4725 as shown below:

So, the prime factorization of 4725 is, 4725 = 3 x 3 x 3 x 5 x 5 x 7.

#### 3. Find factors of 4725 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 4725 would be the two numbers which, when multiplied, give 4725 as the result.

The following table represents the calculation of factors of 4725 in pairs:

Factor Pair Pair Factorization
1 and 4725 1 x 4725 = 4725
3 and 1575 3 x 1575 = 4725
5 and 945 5 x 945 = 4725
7 and 675 7 x 675 = 4725
9 and 525 9 x 525 = 4725
15 and 315 15 x 315 = 4725
21 and 225 21 x 225 = 4725
25 and 189 25 x 189 = 4725
27 and 175 27 x 175 = 4725
35 and 135 35 x 135 = 4725
45 and 105 45 x 105 = 4725
63 and 75 63 x 75 = 4725

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 4725. They are called negative pair factors.

Hence, the negative pairs of 4725 would be ( -1 , -4725 ) , ( -3 , -1575 ) , ( -5 , -945 ) , ( -7 , -675 ) , ( -9 , -525 ) , ( -15 , -315 ) , ( -21 , -225 ) , ( -25 , -189 ) , ( -27 , -175 ) , ( -35 , -135 ) , ( -45 , -105 ) and ( -63 , -75 ) .

#### 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 factor of a number is an exact divisor of that number, example 1, 3, 5, 7, 9, 15, 21, 25, 27, 35, 45, 63, 75, 105, 135, 175, 189, 225, 315, 525, 675, 945, 1575, 4725 are exact divisors of 4725.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 4725 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 4725.

• Which is the smallest prime factor of 4725?

Smallest prime factor of 4725 is 3.

• Is 4725 a perfect square?

No 4725 is not a perfect square.

• What are five multiples of 4725?

First five multiples of 4725 are 9450, 14175, 18900, 23625, 28350.

• What is prime factorization of 4725?

Prime factorization of 4725 is 3 x 3 x 3 x 5 x 5 x 7.

• What are factors of 4725?

Factors of 4725 are 1, 3, 5, 7, 9, 15, 21, 25, 27, 35, 45, 63, 75, 105, 135, 175, 189, 225, 315, 525, 675, 945, 1575, 4725.

• How do you find factors of a negative number? ( eg. -4725 )?

Factors of -4725 are -1, -3, -5, -7, -9, -15, -21, -25, -27, -35, -45, -63, -75, -105, -135, -175, -189, -225, -315, -525, -675, -945, -1575, -4725.

• Is 4725 a whole number?

Yes 4725 is a whole number.

• Which is greatest factor of 4725?

The greatest factor of 4725 is 1575.

• What are the prime factors of 4725?

The factors of 4725 are 1, 3, 5, 7, 9, 15, 21, 25, 27, 35, 45, 63, 75, 105, 135, 175, 189, 225, 315, 525, 675, 945, 1575, 4725.
Prime factors of 4725 are 3, 3, 3, 5, 5, 7.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 4725. Can you help her?

Prime factors of 4725 are 3, 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 4725?

Factors of 4725 are 1, 3, 5, 7, 9, 15, 21, 25, 27, 35, 45, 63, 75, 105, 135, 175, 189, 225, 315, 525, 675, 945, 1575, 4725.
Even factors of 4725 are 0.
Hence, product of even factors of 4725 is; 0 = 0.

Joy wants to calculate mean of all the factors of 4725. Help him in finding the mean of 4725.

Factors of 4725 are 1, 3, 5, 7, 9, 15, 21, 25, 27, 35, 45, 63, 75, 105, 135, 175, 189, 225, 315, 525, 675, 945, 1575, 4725.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 4725 is 1 + 3 + 5 + 7 + 9 + 15 + 21 + 25 + 27 + 35 + 45 + 63 + 75 + 105 + 135 + 175 + 189 + 225 + 315 + 525 + 675 + 945 + 1575 + 4725 = 9920.
Hence, the mean of factors of 4725 is 9920 ÷ 24 = 413.33.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 4725? Help her in writing all the factors.

Positive factors are 1, 3, 5, 7, 9, 15, 21, 25, 27, 35, 45, 63, 75, 105, 135, 175, 189, 225, 315, 525, 675, 945, 1575, 4725.
Negative factors are -1, -3, -5, -7, -9, -15, -21, -25, -27, -35, -45, -63, -75, -105, -135, -175, -189, -225, -315, -525, -675, -945, -1575, -4725.

How many factors are there for 4725?

Factors of 4725 are 1, 3, 5, 7, 9, 15, 21, 25, 27, 35, 45, 63, 75, 105, 135, 175, 189, 225, 315, 525, 675, 945, 1575, 4725.
So there are in total 24 factors.

Joey wants to write all the prime factors of 4725 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 4725 are 3, 3, 3, 5, 5, 7.
So in exponential form it can be written as 33 x 52 x 7.

Kevin has been asked to write 23 factor(s) of 4725. Can you predict the answer?

23 factor(s) of 4725 are 1, 3, 5, 7, 9, 15, 21, 25, 27, 35, 45, 63, 75, 105, 135, 175, 189, 225, 315, 525, 675, 945, 1575.