Factors of 2625

The numbers that divide 2625 evenly are known as factors of 2625.

A factor of 2625 is a number that divides the number without remainder.

The factors of 2625 are 1, 3, 5, 15, 25, 35, 75, 105, 175, 525, 875, and 2625.

Negative factors of 2625: -1, -3, -5, -15, -25, -35, -75, -105, -175, -525, -875, and -2625.

Prime factors of 2625: 3, 5, and 7.

Prime factorization of 2625: \(3^1 \times 5^2 \times 7^1 \times 5^1\).

The sum of factors of 2625: 1 + 3 + 5 + 15 + 25 + 35 + 75 + 105 + 175 + 525 + 875 + 2625 = 4469

Factors can be found using different methods. Mentioned below are some commonly used methods:

• Finding factors using multiplication
   
• Finding factors using division method
   
• Prime factors and Prime factorization

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 2625. Identifying the numbers which are multiplied to get the number 2625 is the multiplication method.

Step 1: Multiply 2625 by 1, 2625 × 1 = 2625.

Step 2: Check for other numbers that give 2625 after multiplying

3 × 875 = 2625

5 × 525 = 2625

15 × 175 = 2625

25 × 105 = 2625

35 × 75 = 2625

Therefore, the positive factor pairs of 2625 are: (1, 2625), (3, 875), (5, 525), (15, 175), (25, 105), (35, 75).

For every positive factor, there is a negative factor.

Dividing the given numbers with the whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following a simple division method -

Step 1: Divide 2625 by 1, 2625 ÷ 1 = 2625.

Step 2: Continue dividing 2625 by the numbers until the remainder becomes 0.

2625 ÷ 1 = 2625

2625 ÷ 3 = 875

2625 ÷ 5 = 525

2625 ÷ 15 = 175

2625 ÷ 25 = 105

2625 ÷ 35 = 75

Therefore, the factors of 2625 are: 1, 3, 5, 15, 25, 35, 75, 105, 175, 525, 875, 2625.

The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:

• Using prime factorization
   
• Using factor tree

Using Prime Factorization: In this process, prime factors of 2625 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

2625 ÷ 3 = 875

875 ÷ 5 = 175

175 ÷ 5 = 35

35 ÷ 7 = 5

5 ÷ 5 = 1

The prime factors of 2625 are 3, 5, and 7.

The prime factorization of 2625 is: \(3^1 \times 5^2 \times 7^1 \times 5^1\).

The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -

Step 1: Firstly, 2625 is divided by 3 to get 875.

Step 2: Now divide 875 by 5 to get 175.

Step 3: Then divide 175 by 5 to get 35.

Step 4: Divide 35 by 7 to get 5.

Here, 5 is the smallest prime number, that cannot be divided anymore.

So, the prime factorization of 2625 is: \(3^1 \times 5^2 \times 7^1 \times 5^1\).

Factor Pairs Two numbers that are multiplied to give a specific number are called factor pairs.

Both positive and negative factors constitute factor pairs.

Positive factor pairs of 2625: (1, 2625), (3, 875), (5, 525), (15, 175), (25, 105), and (35, 75).

Negative factor pairs of 2625: (-1, -2625), (-3, -875), (-5, -525), (-15, -175), (-25, -105), and (-35, -75).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 2625 are 1, 3, 5, 15, etc.
   
• Prime factors: The factors which are prime numbers. For example, 3, 5, and 7 are prime factors of 2625.
   
• Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 2625 are (1, 2625), (3, 875), etc.
   
• Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 2625 is \(3^1 \times 5^2 \times 7^1 \times 5^1\).
   
• Multiples: Numbers obtained by multiplying the original number by whole numbers. For example, 2625 is a multiple of 5.