Factors of 1575

The numbers that divide 1575 evenly are known as factors of 1575. A factor of 1575 is a number that divides the number without remainder. The factors of 1575 include: 1, 3, 5, 7, 9, 15, 21, 25, 35, 45, 63, 75, 105, 175, 225, 315, 525, and 1575.

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

Prime factors of 1575: 3, 5, and 7.

Prime factorization of 1575: 3² × 5² × 7.

The sum of factors of 1575: 1 + 3 + 5 + 7 + 9 + 15 + 21 + 25 + 35 + 45 + 63 + 75 + 105 + 175 + 225 + 315 + 525 + 1575 = 3150

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

1. Finding factors using multiplication
2. Finding factors using division method
3. Prime factors and Prime factorization

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 1575. Identifying the numbers which are multiplied to get the number 1575 is the multiplication method.

Step 1: Multiply 1575 by 1, 1575 × 1 = 1575.

Step 2: Check for other numbers that give 1575 after multiplying:

3 × 525 = 1575

5 × 315 = 1575

7 × 225 = 1575

9 × 175 = 1575

15 × 105 = 1575

21 × 75 = 1575

25 × 63 = 1575

35 × 45 = 1575

Therefore, the positive factor pairs of 1575 are: (1, 1575), (3, 525), (5, 315), (7, 225), (9, 175), (15, 105), (21, 75), (25, 63), (35, 45). 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 in whole numbers as factors. Factors can be calculated by following a simple division method -

Step 1: Divide 1575 by 1, 1575 ÷ 1 = 1575.

Step 2: Continue dividing 1575 by the numbers until the remainder becomes 0.

1575 ÷ 1 = 1575

1575 ÷ 3 = 525

1575 ÷ 5 = 315

1575 ÷ 7 = 225

1575 ÷ 9 = 175

1575 ÷ 15 = 105

1575 ÷ 21 = 75

1575 ÷ 25 = 63

1575 ÷ 35 = 45

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

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 1575 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

1575 ÷ 3 = 525

525 ÷ 3 = 175

175 ÷ 5 = 35

35 ÷ 5 = 7

7 ÷ 7 = 1

The prime factors of 1575 are 3, 5, and 7. The prime factorization of 1575 is: 3^2 × 5^2 × 7.

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

Step 1: Firstly, 1575 is divided by 3 to get 525.

Step 2: Now divide 525 by 3 to get 175.

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

Step 4: Divide 35 by 5 to get 7. Here, 7 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1575 is: 3² × 5² × 7.

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 1575: (1, 1575), (3, 525), (5, 315), (7, 225), (9, 175), (15, 105), (21, 75), (25, 63), (35, 45).

• Negative factor pairs of 1575: (-1, -1575), (-3, -525), (-5, -315), (-7, -225), (-9, -175), (-15, -105), (-21, -75), (-25, -63), (-35, -45).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1575 are 1, 3, 5, 7, etc.

• Prime factors: The factors which are prime numbers. For example, 3, 5, and 7 are prime factors of 1575.

• 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 1575 are (1, 1575), (3, 525), etc.

• Prime factorization: The expression of a number as a product of its prime factors. For instance, 1575 is expressed as 3² × 5² × 7.

• Negative factors: Factors that are negative values of the positive factors. For example, -1, -3, -5, -7, etc., are negative factors of 1575.