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Last updated on ** September 27th, 2024**

Factors of 75 are numbers that can divide 75 completely without the remainder. We often use factors like organizing events and seating arrangements in our daily lives. In this topic, we will know more about the factors of 75 and the different methods to find them.

The factors of 75 are 1, 3, 5, 15, 25 and 75.

**Negative Factors: **These are negative counterparts of the positive factors.

Negative factors: -1, -3, -5, -15, -25, -75

**Prime Factors: **Prime factors are the prime numbers themselves, when multiplied together, give 75 as the product.

Prime factors: 3, 5

**Prime Factorization: **Prime factorization involves breaking 75 into its prime factors

It is expressed as 3^{1} × 5^{2}

Table listing the factors of 75

There are different methods to find the factors of 75.

Methods to find the factors of 75:

- Multiplication Method

- Division Method

- Prime Factor and Prime Factorization

- Factor Tre

The multiplication method finds the pair of factors that give 75 as their product.

**Step 1: **Find the pair of numbers whose product is 75.

**Step 2: **The factors are those numbers, when multiplied, give 75.

**Step 3: **Make a list of numbers whose product will be 75.

A list of numbers whose products are 75 is given below:

- 1 × 75 = 75

- 3 × 25 = 75

- 5 × 15 = 75

The division method finds the numbers that fully divide the given number. steps are given below:

**Step 1: **Since every number is divisible by 1, 1 will always be a factor. Example: 75÷1 = 75

**Step 2: **Move to the next integer. Both divisor and quotient are the factors.

Picture showing the division method:

Overview of Factors of 75 using the division method

Multiplying prime numbers to get the given number as their product is called prime factors. Prime factorization is breaking down the number into its prime factors.

**Prime** **Factors of 75: **Number 75 has only one prime factor.

Prime factors of 75: 3, 5

To find the prime factors of 75, divide 75 with the prime numbers 3 and 5.

**Step 1: **Divide 75 with the prime number 3

75÷3 = 25

**Step 2:** Divide 25 with the prime number 5

25÷5 = 5

5÷5 = 1

**Prime Factorization of 75: **Prime Factorization breaks down the prime factors of 75

Expressed as 3^{1 }× 5^{2}

The prime factorization is visually represented using the factor tree. It helps to understand the process easily. In this factor tree, each branch splits into prime factors.

Factor Tree for 75:

Factors of 75 can be written in both positive pairs and negative pairs. They are like team members. Their product will be equal to the number given.

**Positive Factor Pairs:** (1,75), (3,25), (5,15)

**Negative Factor Pairs:** (-1,-75), (-3,-25), (-5,-15)

**Co-prime:**Numbers having 1 as the only common factor.

**Perfect Square:**The number we get when the same number is multiplied twice.

**Prime Factors:**Prime numbers, which are factors of a given number

**Factor Tree**: A tree diagram used to represent the prime factors of a given number.

**Multiple:**Numbers we get when another number multiplies the given number.