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Factors of 612: Prime Factorization, Methods, and Examples

The number 612 has a total of 12 positive factors and 12 negative factors which means 24 factors in total. All these 24 numbers exist on the number line and belong to the integers. 

When we divide 612 by any of these numbers the answer is never a fraction or decimal 8mber, it should be a whole number.

Factors of 612

Here are the factors of number 612.

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

Negative Factors of 612

The negative factors of 612 are similar to its positive aspects, just with a negative sign.

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

Prime Factorization of 612

The prime factorization of 612 is the way of expressing its prime factors in the product form.

Prime Factorization: 2$^2$ x 3$^2$ x 17

In this article, we will learn about the factors of 612 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the 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, and 612. These numbers are the factors as they do not leave any remainder when divided by 612.

The factors of 612 are classified as prime numbers and composite numbers. The prime factors of the number 612 can be determined using the prime factorization technique.

How To Find the Factors of 612?

You can find the factors of 612 by using the rules of divisibility. The divisibility rule states that any number, when divided by any other natural number, is said to be divisible by the number if the quotient is the whole number and the resulting remainder is zero.

To find the factors of 612, create a list containing the numbers that are exactly divisible by 612 with zero remainders. One important thing to note is that 1 and 612 are the 612’s factors as every natural number has 1 and the number itself as its factor.

1 is also called the universal factor of every number. The factors of 612 are determined as follows:

\[\dfrac{612}{1} = 612\]

\[\dfrac{612}{2} = 306\]

\[\dfrac{612}{3} = 204\]

\[\dfrac{612}{4} = 153\]

\[\dfrac{612}{6} = 102\]

\[\dfrac{612}{9} = 68\]

\[\dfrac{612}{12} = 51\]

\[\dfrac{612}{17} = 36\]

\[\dfrac{612}{18} = 34\]

\[\dfrac{612}{34} = 18\]

\[\dfrac{612}{36} = 17\]

\[\dfrac{612}{51} = e12\]

\[\dfrac{612}{68} = 9\]

\[\dfrac{612}{102} = 6\]

\[\dfrac{612}{153} = 4\]

\[\dfrac{612}{204} = 3\]

\[\dfrac{612}{306} = 2\]

\[\dfrac{612}{612} = 1\]

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

Total Number of Factors of 612

For 612, there are 18 positive factors and 18 negative ones. So in total, there are 36 factors of 612. 

To find the total number of factors of the given number, follow the procedure mentioned below:

  1. Find the factorization/prime factorization of the given number.
  2. Demonstrate the prime factorization of the number in the form of exponent form.
  3. Add 1 to each of the exponents of the prime factor.
  4. Now, multiply the resulting exponents together. This obtained product is equivalent to the total number of factors of the given number.

By following this procedure, the total number of factors of 612 is given as:

Factorization of 612 is 1 x 2$^2$ x 3$^2$ x 17.

The exponent of 1 and 17 is 1 whereas, the exponent of 2 ad 3 is 2.

Adding 1 to each and multiplying them together results in 36.

Therefore, the total number of factors of 612 is 36. 18 are positive, and 18 factors are negative.

Important Notes

Here are some essential points that must be considered while finding the factors of any given number:

  • The factor of any given number must be a whole number.
  • The factors of the number cannot be in the form of decimals or fractions.
  • Factors can be positive as well as negative.
  • Negative factors are the additive inverse of the positive factors of a given number.
  • The factor of a number cannot be greater than that number.
  • Every even number has 2 as its prime factor, the smallest prime factor.

Factors of 612 by Prime Factorization

The number 612 is a composite number. Prime factorization is a valuable technique for finding the number’s prime factors and expressing the number as the product of its prime factors.

Before finding the factors of 612 using prime factorization, let us find out what prime factors are. Prime factors are the factors of any given number that are only divisible by 1 and themselves.

To start the prime factorization of 612, start dividing by its most minor prime factor. First, determine that the given number is either even or odd. If it is an even number, then 2 will be the smallest prime factor.

Continue splitting the quotient obtained until 1 is received as the quotient. The prime factorization of 612 can be expressed as:

612 = 2 x 2 x 3 x 3 x 17

Factors of 612 in Pairs

The factor pairs are the duplet of numbers that, when multiplied together, result in the factorized number. Factor pairs can be more than one depending on the total number of factors given.

For 612, the factor pairs can be found as:

1 x 612 = 612

2 x 306 = 612 

3 x 204 = 612 

4 x 153 = 612 

6 x 102 = 612 

9 x 68= 612 

12 x 51 = 612 

17 x 36 = 612 

18 x 34 = 612 

The possible factor pairs of 612 are given as (1, 612), (2, 306), (3, 204), (4, 153), (6, 102), (9, 68), (12, 51), (17, 36)  and (18, 34).

All these numbers in pairs, when multiplied, give 612 as the product.

The negative factor pairs of 612 are given as:

-1 x -612 = 612

-2 x -306 = 612 

-3 x -204 = 612 

-4 x -153 = 612 

-6 x -102 = 612 

-9 x -68= 612 

-12 x -51 = 612 

-17 x -36 = 612 

-18 x -34 = 612 

It is important to note that in negative factor pairs, the minus sign has been multiplied by the minus sign, due to which the resulting product is the original positive number. Therefore, -1, -2, -3, -4, -6, -9, -12, -17, -18, -34, -36, -51, -68, -102, -153, -204, -306, and -612 are called negative factors of 612.

The list of all the factors of 612, including positive as well as negative numbers, is given below.

Factor list of 612: 1, -1,  2, -2,  3, -3, 4, -4, 6, -6, 9, -9, 12, -12, 17, -17, 18, -18, 34, -34, 36, -36, 51, -51, 68, -68, 102, -102, 153, -153, 204, -204, 306, -306, 612, and -612

Factors of 612 Solved Examples

To better understand the concept of factors, let’s solve some examples.

Example 1

How many factors of 612 are there?

Solution

The total number of Factors of 612 is 18.

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

Example 2

Find the factors of 612 using prime factorization.

Solution

The prime factorization of 612 is given as:

612 $\div$ 2 = 306 

306 $\div$ 2 = 153

153 $\div$ 3 = 51 

51 $\div$ 3 = 17 

17 $\div$ 17 = 1 

So the prime factorization of 153 can be written as:

2$^2$ x 3$^2$ x 17 = 612

Factors of 611|Factors List| Factors of 613

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