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Factors of 525

Factors of 525 are integers that can be divided evenly into 525. There are 12 factors of 525, of which the following are its prime factors 3, 5, 7. The sum of all factors of 525 is 992.

All Factors of 525: 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 175 and 525
Prime Factors of 525: 3, 5, 7
Prime Factorization of 525: 3¹ × 5² × 7¹
Sum of Factors of 525: 992

1.	What Are the Factors of 525?
2.	Factors of 525 by Prime Factorization
3.	Factors of 525 in Pairs
4.	FAQs on Factors of 525

What are Factors of 525?

Factors of 525 are pairs of those numbers whose products result in 525. These factors are either prime numbers or composite numbers.

How to Find the Factors of 525?

To find the factors of 525, we will have to find the list of numbers that would divide 525 without leaving any remainder.

525/15 = 35; therefore, 15 is a factor of 525 and 35 is also a factor of 525.
525/21 = 25; therefore, 21 is a factor of 525 and 25 is also a factor of 525.

Similarly we can find other factors. Hence, the factors of 525 are 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 175, 525.

☛ Also Check:

Factors of 52 - The factors of 52 are 1, 2, 4, 13, 26, 52
Factors of 21 - The factors of 21 are 1, 3, 7, 21
Factors of 32 - The factors of 32 are 1, 2, 4, 8, 16, 32
Factors of 128 - The factors of 128 are 1, 2, 4, 8, 16, 32, 64, 128
Factors of 6 - The factors of 6 are 1, 2, 3, 6

Factors of 525 by Prime Factorization

The number 525 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 525. The first step is to divide the number 525 with the smallest prime factor, here it is 3. We keep dividing until it gives a non-zero remainder.

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 525 can be written as 3¹ × 5² × 7¹ where 3, 5, 7 are prime.

Factors of 525 in Pairs

Pair factors of 525 are the pairs of numbers that when multiplied give the product 525. The factors of 525 in pairs are:

1 × 525 = (1, 525)
3 × 175 = (3, 175)
5 × 105 = (5, 105)
7 × 75 = (7, 75)
15 × 35 = (15, 35)
21 × 25 = (21, 25)

Negative pair factors of 525 are:

-1 × -525 = (-1, -525)
-3 × -175 = (-3, -175)
-5 × -105 = (-5, -105)
-7 × -75 = (-7, -75)
-15 × -35 = (-15, -35)
-21 × -25 = (-21, -25)

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

Factors of 525 Solved Examples

Example 1: How many factors are there for 525?

Solution:

The factors of 525 are too many, therefore if we can find the prime factorization of 525, 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 525 = 3¹ × 5² × 7¹
Therefore, the total number of factors are (1 + 1) × (2 + 1) × (1 + 1) = 2 × 3 × 2 = 12
Example 2: Find the Least Common Multiple (LCM) and Highest Common Factor (HCF) of 525 and 264.

Solution:

The factors of 525 are 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 175, 525 and factors of 264 are 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, 264.

Therefore, the Least Common Multiple (LCM) of 525 and 264 is 46200 and Highest Common Factor (HCF) of 525 and 264 is 3.
Example 3: Find if 3, 7, 15, 21, 35, 75 and 342 are factors of 525.

Solution:

When we divide 525 by 342 it leaves a remainder. Therefore, the number 342 is not a factor of 525. All numbers except 342 are factors of 525.
Example 4: Find the product of all the prime factors of 525.

Solution:

Since, the prime factors of 525 are 3, 5, 7. Therefore, the product of prime factors = 3 × 5 × 7 = 105.

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FAQs on Factors of 525

What are the Factors of 525?

The factors of 525 are 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 175, 525 and its negative factors are -1, -3, -5, -7, -15, -21, -25, -35, -75, -105, -175, -525.

What is the Sum of the Factors of 525?

Sum of all factors of 525 = (3^{1 + 1} - 1)/(3 - 1) × (5^{2 + 1} - 1)/(5 - 1) × (7^{1 + 1} - 1)/(7 - 1) = 992

What are the Pair Factors of 525?

The pair factors of 525 are (1, 525), (3, 175), (5, 105), (7, 75), (15, 35), (21, 25).

What is the Greatest Common Factor of 525 and 236?

The factors of 525 are 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 175, 525 and the factors of 236 are 1, 2, 4, 59, 118, 236. 525 and 236 have only one common factor which is 1. This implies that 525 and 236 are co-prime.

Hence, the Greatest Common Factor (GCF) of 525 and 236 is 1.

What are the Common Factors of 525 and 336?

Since, the factors of 525 are 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 175, 525 and the factors of 336 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336.
Hence, [1, 3, 7, 21] are the common factors of 525 and 336.

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