Factors of 75 | Prime Factorization of 75 | Factor Tree of 75

Factors of 75

Factors of 75	Factor Pairs of 75	Prime factors of 75
1, 3, 5, 15, 25, 75	(1,75) (3,25) (5,15) (15,5) (25,3)	3 x 5 x 5

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What are the factors of 75

The factors of 75 are the numbers that divide evenly the number 75. They are:1, 3, 5, 15, 25, and 75

To find the factors of a number, you can start by dividing it by the smallest possible factor (which is usually 2) and then continue dividing by the next smallest prime numbers (3, 5, 7, etc.) until you can’t divide anymore. Alternatively, you can use a factorization tree or the prime factorization of the number to find its factors.

How to Find Factors of 75

To find the factors of 75, you can follow any of 6these methods: 

1. Factors of 75 using the Multiplication Method
2. Factors of 75 using the Division Method
3. Prime Factorization of 75
4. Factor tree of 75

Factors of 75 Using the Multiplication Method

• One way to find the factors of 75 is to list out all the pairs of numbers that multiply to give 75.
• The factors of 75 will be all the numbers that appear in these pairs.
• For example, if we list out the pairs of numbers that multiply to give 75, we get: (1, 75), (3, 25), and (5, 15).
• Therefore, the factors of 75 are 1, 3, 5, 15, 25, and 75.
• This method works because if two numbers multiply to give a third number, then the third number is a multiple of the first two numbers.

Factors of 75 Using the Division Method

• To find the factors of 75 using the division method, start by dividing 75 by the smallest possible factor (usually 2).
• If the result is an integer, then that number is a factor of 75.
• If the result is not an integer, divide it by the next smallest prime number (3).
• Continue dividing by the next smallest prime numbers (4, 5, 6, etc.) until you reach a result that is an integer.
• The integer results are the factors of 75.

For example:

• 75 / 2 = 37.5 (not an integer)
• 75 / 3 = 25 (an integer)

Therefore, the factors of 75 are 3 and 25. This method works because if a number is a factor of 75, then 75 will divide evenly by that number.

Prime Factorization of 75

• The prime factorization of 75 can be found by breaking it down into its prime factors.
• To begin, we divide 75 by the smallest prime number, which is 2. However, 75 is not divisible by 2.
• Next, we divide 75 by the next prime number, which is 3. 75 divided by 3 equals 25.
• Now, we divide 25 by the next prime number, which is also 5. 25 divided by 5 equals 5.
• At this point, we have obtained the prime factorization of 75:
• 75 = 3 x 5 x 5
• Therefore, the prime factorization of 75 is 3 x 5 x 5.

Factor tree of 75

To create a factor tree, we start by writing the number we want to factor at the top of the tree. In this case, that number is 75. We then find two numbers that multiply together to equal 75 and write them as the children of the top node. In this case, those numbers are 5 and 15.

Next, we repeat this process for each of the children. For the child node with the value of 15, we find two numbers that multiply by 15 and write those as the children of the 15 nodes. In this case, those numbers are 5 and 3.

We continue this process until all of the nodes are prime numbers. When we are finished, our factor tree looks like this:

This factor tree shows that 75 can be written as the product of the prime numbers 3 and 5, or as 3 x 5 x 5, which is the prime factorization of 75.

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Factor Pairs of 75

The factor pairs of a number are the pairs of numbers that can be multiplied together to equal that number. To find the factor pairs of 75, we can list out all of the numbers that 75 can be evenly divided by, along with the result of the division. These numbers are 1, 3, and 5.

The corresponding factor pairs for 75 are (1, 75), (3, 25), and (5, 15). These are the pairs of numbers that multiply together to give us 75. For example, the factor pair (1, 75) means that 1 and 75 can be multiplied together to equal 75. The factor pair (3, 25) means that 3 and 25 can be multiplied together to equal 75. And the factor pair (5, 15) means that 5 and 15 can be multiplied together to equal 75.

More factors

• Factors of 72
• Factors of 73
• Factors of 74
• Factors of 75
• Factors of 76
• Factors of 77
• Factors of 78

Factors of 75 – Quick Recap

• Factors of 75: 1, 3, 5, 15, 25, 75
• Negative Factors of 75: -1, -3, -5, -15, -25, -75
• Prime Factors of 75:  3 × 5 × 5
• Prime Factorization of 75: 3 × 5 × 5

Factors of 75 – Fun Facts

• 75 is a composite number, which means it has more than two factors. In addition to 1 and itself, 75 has three other positive integer factors: 3, 5, and 15.
• 75 is the smallest number that has three distinct prime factors. Its prime factorization is 3 x 5 x 5.
• The factors of 75 can be used to make a variety of interesting patterns when they are arranged in a grid. For example, you can create a 3×5 grid by multiplying the factors 3 and 5 together, or a 5×5 grid by multiplying the factors 5 and 5 together.
• The factors of 75 can be used to make interesting shapes when they are plotted on a coordinate plane. For example, you can plot the factors of 75 as points on a grid and connect them to create polygons.

Also Check: Multiples, Square Root, and LCM

Solved Examples of Factor of 75

Q.1: If a number is divisible by five and three, what is the greatest common factor of that number?
Solution: The greatest common factor (GCF) of a number that is divisible by five and three is 15, as both 5 and 3 are divisible by 15 without a remainder.

Q.2: Is 74 a multiple of 75? 
Solution: No, 74 is not a multiple of 75 since 75 does not divide into 74 evenly.

Q.3: What two numbers add up to 75?
Solution: Two numbers that add up to 75 include 28 and 47; 28 + 47 = 75.

Q.4: What is the product of all positive integer divisors for 75?
Solution: The product of all positive integer divisors for 75 is 421,875; 1 x 3 x 5 x 15 x 25 x75 = 421,875.

Q.5: What two prime factors added together equal 74?
Solution: Two prime factors that added together equal 74 include 37 and 37; 37 + 37 = 74.  

Q.6: What three numbers multiplied together equal 75?    
Solution: Three numbers multiplied together to equal 75 are 3,5 and 5; 3 x5x5=75.  

Q.7: What Are Some Examples Of Factors Of 75?     
Solution: Some examples of factors of 7 5 include1,3,5,15,25, and 75 .  

Q.8:  How do you calculate the LCM (Least Common Multiple) of 75?     
Solution: To find the least common multiple (LCM) of 75, we need to determine the prime factorization of 75. The prime factorization of 75 is 3 x 5 x 5. To calculate the LCM, we take the highest power of each prime factor that appears in the factorization. In this case, we have 3 and two 5s. LCM of 75 = (Highest power of 3) x (Highest power of 5)Highest power of 3 = 3^1 = 3 Highest power of 5 = 5^2 = 25. LCM of 75 = 3 x 25 = 75

Therefore, the least common multiple (LCM) of 75 is 75.

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Frequently Asked Questions on Factors of 75