# Factors of 1224

Factors of 1224 are 1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 68, 72, 102, 136, 153, 204, 306, 408, 612, and 1224

#### How to find factors of a number

 1.   Find factors of 1224 using Division Method 2.   Find factors of 1224 using Prime Factorization 3.   Find factors of 1224 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 1224

• Divide 1224 by 1: 1224 ÷ 1 : Remainder = 0
• Divide 1224 by 2: 1224 ÷ 2 : Remainder = 0
• Divide 1224 by 3: 1224 ÷ 3 : Remainder = 0
• Divide 1224 by 4: 1224 ÷ 4 : Remainder = 0
• Divide 1224 by 6: 1224 ÷ 6 : Remainder = 0
• Divide 1224 by 8: 1224 ÷ 8 : Remainder = 0
• Divide 1224 by 9: 1224 ÷ 9 : Remainder = 0
• Divide 1224 by 12: 1224 ÷ 12 : Remainder = 0
• Divide 1224 by 17: 1224 ÷ 17 : Remainder = 0
• Divide 1224 by 18: 1224 ÷ 18 : Remainder = 0
• Divide 1224 by 24: 1224 ÷ 24 : Remainder = 0
• Divide 1224 by 34: 1224 ÷ 34 : Remainder = 0
• Divide 1224 by 36: 1224 ÷ 36 : Remainder = 0
• Divide 1224 by 51: 1224 ÷ 51 : Remainder = 0
• Divide 1224 by 68: 1224 ÷ 68 : Remainder = 0
• Divide 1224 by 72: 1224 ÷ 72 : Remainder = 0
• Divide 1224 by 102: 1224 ÷ 102 : Remainder = 0
• Divide 1224 by 136: 1224 ÷ 136 : Remainder = 0
• Divide 1224 by 153: 1224 ÷ 153 : Remainder = 0
• Divide 1224 by 204: 1224 ÷ 204 : Remainder = 0
• Divide 1224 by 306: 1224 ÷ 306 : Remainder = 0
• Divide 1224 by 408: 1224 ÷ 408 : Remainder = 0
• Divide 1224 by 612: 1224 ÷ 612 : Remainder = 0
• Divide 1224 by 1224: 1224 ÷ 1224 : Remainder = 0

Hence, Factors of 1224 are 1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 68, 72, 102, 136, 153, 204, 306, 408, 612, and 1224

#### 2. Steps to find factors of 1224 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 1224 using the division method, follow these steps:

• Step 1. Start dividing 1224 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 1224, which is 2. Divide 1224 by 2 to obtain the quotient (612).
1224 ÷ 2 = 612
• Step 3. Repeat step 1 with the obtained quotient (612).
612 ÷ 2 = 306
306 ÷ 2 = 153
153 ÷ 3 = 51
51 ÷ 3 = 17
17 ÷ 17 = 1

So, the prime factorization of 1224 is, 1224 = 2 x 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 1224 as shown below:

So, the prime factorization of 1224 is, 1224 = 2 x 2 x 2 x 3 x 3 x 17.

#### 3. Find factors of 1224 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 1224 would be the two numbers which, when multiplied, give 1224 as the result.

The following table represents the calculation of factors of 1224 in pairs:

Factor Pair Pair Factorization
1 and 1224 1 x 1224 = 1224
2 and 612 2 x 612 = 1224
3 and 408 3 x 408 = 1224
4 and 306 4 x 306 = 1224
6 and 204 6 x 204 = 1224
8 and 153 8 x 153 = 1224
9 and 136 9 x 136 = 1224
12 and 102 12 x 102 = 1224
17 and 72 17 x 72 = 1224
18 and 68 18 x 68 = 1224
24 and 51 24 x 51 = 1224
34 and 36 34 x 36 = 1224

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 1224. They are called negative pair factors.

Hence, the negative pairs of 1224 would be ( -1 , -1224 ) , ( -2 , -612 ) , ( -3 , -408 ) , ( -4 , -306 ) , ( -6 , -204 ) , ( -8 , -153 ) , ( -9 , -136 ) , ( -12 , -102 ) , ( -17 , -72 ) , ( -18 , -68 ) , ( -24 , -51 ) and ( -34 , -36 ) .

#### How can we define factors?

In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 1224 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 1224.
• Every number is a factor of zero (0), since 1224 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, 8, 9, 12, 17, 18, 24, 34, 36, 51, 68, 72, 102, 136, 153, 204, 306, 408, 612, 1224 are exact divisors of 1224.
• Factors of 1224 are 1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 68, 72, 102, 136, 153, 204, 306, 408, 612, 1224. Each factor divides 1224 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 68, 72, 102, 136, 153, 204, 306, 408, 612, 1224 are all less than or equal to 1224.

• Which is the smallest prime factor of 1224?

Smallest prime factor of 1224 is 2.

• Is 1224 a perfect square?

No 1224 is not a perfect square.

• What are five multiples of 1224?

First five multiples of 1224 are 2448, 3672, 4896, 6120, 7344.

• What is prime factorization of 1224?

Prime factorization of 1224 is 2 x 2 x 2 x 3 x 3 x 17.

• What are factors of 1224?

Factors of 1224 are 1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 68, 72, 102, 136, 153, 204, 306, 408, 612, 1224.

• How do you find factors of a negative number? ( eg. -1224 )?

Factors of -1224 are -1, -2, -3, -4, -6, -8, -9, -12, -17, -18, -24, -34, -36, -51, -68, -72, -102, -136, -153, -204, -306, -408, -612, -1224.

• Is 1224 a whole number?

Yes 1224 is a whole number.

• Which is greatest factor of 1224?

The greatest factor of 1224 is 612.

• What are the prime factors of 1224?

The factors of 1224 are 1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 68, 72, 102, 136, 153, 204, 306, 408, 612, 1224.
Prime factors of 1224 are 2, 2, 2, 3, 3, 17.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 1224. Can you help her?

Prime factors of 1224 are 2, 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 1224?

Factors of 1224 are 1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 68, 72, 102, 136, 153, 204, 306, 408, 612, 1224.
Even factors of 1224 are 2, 4, 6, 8, 12, 18, 24, 34, 36, 68, 72, 102, 136, 204, 306, 408, 612, 1224.
Hence, product of even factors of 1224 is; 2 x 4 x 6 x 8 x 12 x 18 x 24 x 34 x 36 x 68 x 72 x 102 x 136 x 204 x 306 x 408 x 612 x 1224 = 3.157204559052089e+30.

Joy wants to calculate mean of all the factors of 1224. Help him in finding the mean of 1224.

Factors of 1224 are 1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 68, 72, 102, 136, 153, 204, 306, 408, 612, 1224.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 1224 is 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 17 + 18 + 24 + 34 + 36 + 51 + 68 + 72 + 102 + 136 + 153 + 204 + 306 + 408 + 612 + 1224 = 3510.
Hence, the mean of factors of 1224 is 3510 ÷ 24 = 146.25.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 1224? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 68, 72, 102, 136, 153, 204, 306, 408, 612, 1224.
Negative factors are -1, -2, -3, -4, -6, -8, -9, -12, -17, -18, -24, -34, -36, -51, -68, -72, -102, -136, -153, -204, -306, -408, -612, -1224.

How many factors are there for 1224?

Factors of 1224 are 1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 68, 72, 102, 136, 153, 204, 306, 408, 612, 1224.
So there are in total 24 factors.

Joey wants to write all the prime factors of 1224 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1224 are 2, 2, 2, 3, 3, 17.
So in exponential form it can be written as 23 x 32 x 17.

Kevin has been asked to write 23 factor(s) of 1224. Can you predict the answer?

23 factor(s) of 1224 are 1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 68, 72, 102, 136, 153, 204, 306, 408, 612.