Factors of 387

We will now learn about the factors of 387. The factors of 387 can be found in a very simple way:

by identifying numbers that divide 387 without leaving any remainder. The factors of 387 are 1, 3, 9, 43, 129, and 387. Every number has both positive and negative factors. Negative factors are the ones with a negative sign that divides the number without leaving a remainder.

• Negative factors of 387: -1, -3, -9, -43, -129, and -387.

• Prime factors of 387: 3 and 43.

• Prime factorization of 387: 3² x 43

• The sum of factors of 387: 1 + 3 + 9 + 43 + 129 + 387 = 572.

There are different methods we use to find the factors of a number. The most commonly used are as follows:

1. Use of Multiplication Method
2. Use of Division Method
3. Use of Prime Factors and Prime Factorization.

We’ll now look into each of these in detail.

To find the factors of 387 using the multiplication method, simply identify the numbers that can be multiplied to get the value 387.

Step 1: Identify and multiply the pairs of numbers that can give the value of 387.

Multiply 387 with 1 and then repeat the process by multiplying 387 with other numbers.

• 1 × 387 = 387
• 3 × 129 = 387
• 9 × 43 = 387

Step 2: After the calculation, we get these numbers as the factors of 387.

Step 3: The positive factor pairs of 387 found through multiplication are (1, 387), (3, 129), and (9, 43)

Step 4: For every positive factor, there is a corresponding negative factor. So the negative factor pairs of 387 are written as (-1, -387), (-3, -129), and (-9, -43).
 

We can find the factors using the division method. First, divide the target number by 1. Then proceed to divide by every number up to the number itself. See if the division leaves no remainder.

Let's calculate it as given below:

Step 1: Divide 387 by smaller numbers and see if it leaves any remainder. E.g., 387/1 = 387. 

Step 2: We will continue in the same way and check for other numbers as well. Factors of 387 are 1, 3, 9, 43, 129, and 387. They are the factors of 387 because the said number can be divided evenly by these numbers.

The prime factors of 387 are 3 and 43. The prime factors can be determined using the methods as follows:

By Using Prime Factorization: Prime factorization is used to find the factors of the target number by breaking it down into its prime factors. 

2 is the smallest prime number, so begin by dividing by 2. Then, continue dividing by other prime numbers.

• 387 ÷ 3 = 129
• 129 ÷ 3 = 43

43 is a prime number that cannot be further divided.

So, the prime factorization of 387 is: 

387 =  3² x 43

Imagine a tree of numbers with many branches. Each branch is assigned the task of breaking down a number into its prime factors. This visual representation is known as the factor tree.

Step 1: 387 divided by 3 gives us the quotient 129

387 ÷ 3 = 129

Step 2:  Divide 129 by 3 again, which gives us the quotient 43.

Step 3: Since 43 is a prime number, it cannot be divided further.]

The prime factorization of 387 is written below : 

 387 = 3² × 43

Factor pairs are two numbers that, when multiplied together, give the target number. Every number has both positive and negative factor pairs. Let’s look at these sets of factors.

Positive factor pairs: (1, 387), (3, 129), and (9, 43)

Negative factor pairs: (−1, −387), (−3, −129), and (−9, −43)

• Prime Factorization: It is the process of breaking a number down into its prime factors. Prime factors are prime numbers that divide a given number evenly without leaving a remainder. Eg., 387 = 32 x 43

• Remainder: The remainder is what is left when one number is divided by another and the result is not zero. Eg., Divide 17 by 5. 17 divided by 5 = 3 with a remainder of 2.

• Negative Factors: Negative factors are the negative counterparts of positive factors of a number. Eg., -1, -3, -9, -43, -129, and -387 are the negative factors of 387.

• Factor Pairs: The two numbers, when multiplied together, that give the target number are known as factor pairs. They are called factor pairs because each number in the pair divides the target number without leaving a remainder. Eg., the factor pairs of 18 are (1, 18), (2,9) and (3,6)

• Multiplication: Multiplication is the method of finding the product of 2 or more numbers. Eg., product of 3 and 6 is 3 x 6 = 18