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Factors of 4725

Factors of 4725 are numbers that, when multiplied in pairs give the product as 4725. There are overall 24 factors of 4725, of which 3, 5, 7 are its prime factors. The Prime Factorization of 4725 is 3³ × 5² × 7¹.

All Factors of 4725: 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
Prime Factors of 4725: 3, 5, 7
Prime Factorization of 4725: 3³ × 5² × 7¹
Sum of Factors of 4725: 9920

1.	What Are the Factors of 4725?
2.	Factors of 4725 by Prime Factorization
3.	Factors of 4725 in Pairs
4.	FAQs on Factors of 4725

What are Factors of 4725?

Factors of 4725 are pairs of those numbers whose products result in 4725. These factors are either prime numbers or composite numbers.

How to Find the Factors of 4725?

To find the factors of 4725, we will have to find the list of numbers that would divide 4725 without leaving any remainder.

4725/75 = 63; therefore, 75 is a factor of 4725 and 63 is also a factor of 4725.
4725/945 = 5; therefore, 945 is a factor of 4725 and 5 is also a factor of 4725.

Similarly we can find other factors. Hence, 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.

☛ Also Check:

Factors of 19 - The factors of 19 are 1, 19
Factors of 23 - The factors of 23 are 1, 23
Factors of 34 - The factors of 34 are 1, 2, 17, 34
Factors of 29 - The factors of 29 are 1, 29
Factors of 28 - The factors of 28 are 1, 2, 4, 7, 14, 28

Factors of 4725 by Prime Factorization

The number 4725 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 4725. The first step is to divide the number 4725 with the smallest prime factor, here it is 3. We keep dividing until it gives a non-zero remainder.

4725 ÷ 3 = 1575
1575 ÷ 3 = 525
525 ÷ 3 = 175

Further dividing 175 by 3 gives a non-zero remainder. So we stop the process and continue dividing the number 175 by the next smallest prime factor. We stop ultimately if the next prime factor doesn't exist or when we can't divide any further.

So, the prime factorization of 4725 can be written as 3³ × 5² × 7¹ where 3, 5, 7 are prime.

Factors of 4725 in Pairs

Pair factors of 4725 are the pairs of numbers that when multiplied give the product 4725. The factors of 4725 in pairs are:

1 × 4725 = (1, 4725)
3 × 1575 = (3, 1575)
5 × 945 = (5, 945)
7 × 675 = (7, 675)
9 × 525 = (9, 525)
15 × 315 = (15, 315)
21 × 225 = (21, 225)
25 × 189 = (25, 189)
27 × 175 = (27, 175)
35 × 135 = (35, 135)
45 × 105 = (45, 105)
63 × 75 = (63, 75)

Negative pair factors of 4725 are:

-1 × -4725 = (-1, -4725)
-3 × -1575 = (-3, -1575)
-5 × -945 = (-5, -945)
-7 × -675 = (-7, -675)
-9 × -525 = (-9, -525)
-15 × -315 = (-15, -315)
-21 × -225 = (-21, -225)
-25 × -189 = (-25, -189)
-27 × -175 = (-27, -175)
-35 × -135 = (-35, -135)
-45 × -105 = (-45, -105)
-63 × -75 = (-63, -75)

NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.

Factors of 4725 Solved Examples

Example 1: How many factors are there for 4725?

Solution:

The factors of 4725 are too many, therefore if we can find the prime factorization of 4725, then the total number of factors can be calculated using the formula shown below.
If the prime factorization of the number is a^x × b^y × c^z where a, b, c are prime, then the total number of factors can be given by (x + 1)(y + 1)(z + 1).

Prime Factorization of 4725 = 3³ × 5² × 7¹
Therefore, the total number of factors are (3 + 1) × (2 + 1) × (1 + 1) = 4 × 3 × 2 = 24
Example 2: Find the LCM and Greatest Common Divisor (GCD) of 4725 and 4238.

Solution:

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 and factors of 4238 are 1, 2, 13, 26, 163, 326, 2119, 4238.

Therefore, the LCM of 4725 and 4238 is 20024550 and Greatest Common Divisor (GCD) of 4725 and 4238 is 1.
Example 3: Find if 27, 35, 189, 315, 675, 945, 1575 and 4725 are factors of 4725.

Solution:

When we divide 4725 by 27, 35, 189, 315, 675, 945, 1575, 4725 it doesn't leave any remainder. Therefore, 27, 35, 189, 315, 675, 945, 1575, 4725 are factors of 4725.
Example 4: Find the product of all the prime factors of 4725.

Solution:

Since, the prime factors of 4725 are 3, 5, 7. Therefore, the product of prime factors = 3 × 5 × 7 = 105.

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FAQs on Factors of 4725

What are the 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 and its 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.

What is the Sum of Factors of 4725?

Sum of all factors of 4725 = (3^{3 + 1} - 1)/(3 - 1) × (5^{2 + 1} - 1)/(5 - 1) × (7^{1 + 1} - 1)/(7 - 1) = 9920

What Numbers are the Prime Factors of 4725?

The prime factors of 4725 are 3, 5, 7.

What is the Greatest Common Factor of 4725 and 1670?

The factors of 4725 and 1670 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 and 1, 2, 5, 10, 167, 334, 835, 1670 respectively.

Common factors of 4725 and 1670 are [1, 5].

Hence, the Greatest Common Factor (GCF) of 4725 and 1670 is 5.

How Many Factors of 2754 are also common to the Factors of 4725?

Since, 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 and the factors of 2754 are 1, 2, 3, 6, 9, 17, 18, 27, 34, 51, 54, 81, 102, 153, 162, 306, 459, 918, 1377, 2754.
Hence, [1, 3, 9, 27] are the common factors of 4725 and 2754.

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