# Factors of 612

Factors of 612 are 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, and 612

#### How to find factors of a number

 1.   Find factors of 612 using Division Method 2.   Find factors of 612 using Prime Factorization 3.   Find factors of 612 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 612

• Divide 612 by 1: 612 ÷ 1 : Remainder = 0
• Divide 612 by 2: 612 ÷ 2 : Remainder = 0
• Divide 612 by 3: 612 ÷ 3 : Remainder = 0
• Divide 612 by 4: 612 ÷ 4 : Remainder = 0
• Divide 612 by 6: 612 ÷ 6 : Remainder = 0
• Divide 612 by 9: 612 ÷ 9 : Remainder = 0
• Divide 612 by 12: 612 ÷ 12 : Remainder = 0
• Divide 612 by 17: 612 ÷ 17 : Remainder = 0
• Divide 612 by 18: 612 ÷ 18 : Remainder = 0
• Divide 612 by 34: 612 ÷ 34 : Remainder = 0
• Divide 612 by 36: 612 ÷ 36 : Remainder = 0
• Divide 612 by 51: 612 ÷ 51 : Remainder = 0
• Divide 612 by 68: 612 ÷ 68 : Remainder = 0
• Divide 612 by 102: 612 ÷ 102 : Remainder = 0
• Divide 612 by 153: 612 ÷ 153 : Remainder = 0
• Divide 612 by 204: 612 ÷ 204 : Remainder = 0
• Divide 612 by 306: 612 ÷ 306 : Remainder = 0
• Divide 612 by 612: 612 ÷ 612 : Remainder = 0

Hence, Factors of 612 are 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, and 612

#### 2. Steps to find factors of 612 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 612 using the division method, follow these steps:

• Step 1. Start dividing 612 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 612, which is 2. Divide 612 by 2 to obtain the quotient (306).
612 ÷ 2 = 306
• Step 3. Repeat step 1 with the obtained quotient (306).
306 ÷ 2 = 153
153 ÷ 3 = 51
51 ÷ 3 = 17
17 ÷ 17 = 1

So, the prime factorization of 612 is, 612 = 2 x 2 x 3 x 3 x 17.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 612 as shown below:

So, the prime factorization of 612 is, 612 = 2 x 2 x 3 x 3 x 17.

#### 3. Find factors of 612 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 612 would be the two numbers which, when multiplied, give 612 as the result.

The following table represents the calculation of factors of 612 in pairs:

Factor Pair Pair Factorization
1 and 612 1 x 612 = 612
2 and 306 2 x 306 = 612
3 and 204 3 x 204 = 612
4 and 153 4 x 153 = 612
6 and 102 6 x 102 = 612
9 and 68 9 x 68 = 612
12 and 51 12 x 51 = 612
17 and 36 17 x 36 = 612
18 and 34 18 x 34 = 612

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 612. They are called negative pair factors.

Hence, the negative pairs of 612 would be ( -1 , -612 ) , ( -2 , -306 ) , ( -3 , -204 ) , ( -4 , -153 ) , ( -6 , -102 ) , ( -9 , -68 ) , ( -12 , -51 ) , ( -17 , -36 ) and ( -18 , -34 ) .

#### How do you explain factors?

In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 612 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 612.
• Every number is a factor of zero (0), since 612 x 0 = 0.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, 612 are exact divisors of 612.
• Factors of 612 are 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, 612. Each factor divides 612 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, 612 are all less than or equal to 612.

• Which is the smallest prime factor of 612?

Smallest prime factor of 612 is 2.

• Is 612 a perfect square?

No 612 is not a perfect square.

• What are five multiples of 612?

First five multiples of 612 are 1224, 1836, 2448, 3060, 3672.

• What is prime factorization of 612?

Prime factorization of 612 is 2 x 2 x 3 x 3 x 17.

• What are factors of 612?

Factors of 612 are 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, 612.

• How do you find factors of a negative number? ( eg. -612 )?

Factors of -612 are -1, -2, -3, -4, -6, -9, -12, -17, -18, -34, -36, -51, -68, -102, -153, -204, -306, -612.

• Is 612 a whole number?

Yes 612 is a whole number.

• Which is greatest factor of 612?

The greatest factor of 612 is 306.

• What are the prime factors of 612?

The factors of 612 are 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, 612.
Prime factors of 612 are 2, 2, 3, 3, 17.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 612. Can you help her?

Prime factors of 612 are 2, 2, 3, 3, 17.
Hence, the product of prime factors of 102.

Can you help Rubel to find out the product of the even factors of 612?

Factors of 612 are 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, 612.
Even factors of 612 are 2, 4, 6, 12, 18, 34, 36, 68, 102, 204, 306, 612.
Hence, product of even factors of 612 is; 2 x 4 x 6 x 12 x 18 x 34 x 36 x 68 x 102 x 204 x 306 x 612 = 3362702965323596000.

Joy wants to calculate mean of all the factors of 612. Help him in finding the mean of 612.

Factors of 612 are 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, 612.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 612 is 1 + 2 + 3 + 4 + 6 + 9 + 12 + 17 + 18 + 34 + 36 + 51 + 68 + 102 + 153 + 204 + 306 + 612 = 1638.
Hence, the mean of factors of 612 is 1638 ÷ 18 = 91.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 612? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, 612.
Negative factors are -1, -2, -3, -4, -6, -9, -12, -17, -18, -34, -36, -51, -68, -102, -153, -204, -306, -612.

How many factors are there for 612?

Factors of 612 are 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, 612.
So there are in total 18 factors.

Joey wants to write all the prime factors of 612 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 612 are 2, 2, 3, 3, 17.
So in exponential form it can be written as 22 x 32 x 17.

Kevin has been asked to write 17 factor(s) of 612. Can you predict the answer?

17 factor(s) of 612 are 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306.