# Factors of 1428

Factors of 1428 are 1, 2, 3, 4, 6, 7, 12, 14, 17, 21, 28, 34, 42, 51, 68, 84, 102, 119, 204, 238, 357, 476, 714, and 1428

#### How to find factors of a number

 1.   Find factors of 1428 using Division Method 2.   Find factors of 1428 using Prime Factorization 3.   Find factors of 1428 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 1428

• Divide 1428 by 1: 1428 ÷ 1 : Remainder = 0
• Divide 1428 by 2: 1428 ÷ 2 : Remainder = 0
• Divide 1428 by 3: 1428 ÷ 3 : Remainder = 0
• Divide 1428 by 4: 1428 ÷ 4 : Remainder = 0
• Divide 1428 by 6: 1428 ÷ 6 : Remainder = 0
• Divide 1428 by 7: 1428 ÷ 7 : Remainder = 0
• Divide 1428 by 12: 1428 ÷ 12 : Remainder = 0
• Divide 1428 by 14: 1428 ÷ 14 : Remainder = 0
• Divide 1428 by 17: 1428 ÷ 17 : Remainder = 0
• Divide 1428 by 21: 1428 ÷ 21 : Remainder = 0
• Divide 1428 by 28: 1428 ÷ 28 : Remainder = 0
• Divide 1428 by 34: 1428 ÷ 34 : Remainder = 0
• Divide 1428 by 42: 1428 ÷ 42 : Remainder = 0
• Divide 1428 by 51: 1428 ÷ 51 : Remainder = 0
• Divide 1428 by 68: 1428 ÷ 68 : Remainder = 0
• Divide 1428 by 84: 1428 ÷ 84 : Remainder = 0
• Divide 1428 by 102: 1428 ÷ 102 : Remainder = 0
• Divide 1428 by 119: 1428 ÷ 119 : Remainder = 0
• Divide 1428 by 204: 1428 ÷ 204 : Remainder = 0
• Divide 1428 by 238: 1428 ÷ 238 : Remainder = 0
• Divide 1428 by 357: 1428 ÷ 357 : Remainder = 0
• Divide 1428 by 476: 1428 ÷ 476 : Remainder = 0
• Divide 1428 by 714: 1428 ÷ 714 : Remainder = 0
• Divide 1428 by 1428: 1428 ÷ 1428 : Remainder = 0

Hence, Factors of 1428 are 1, 2, 3, 4, 6, 7, 12, 14, 17, 21, 28, 34, 42, 51, 68, 84, 102, 119, 204, 238, 357, 476, 714, and 1428

#### 2. Steps to find factors of 1428 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 1428 using the division method, follow these steps:

• Step 1. Start dividing 1428 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 1428, which is 2. Divide 1428 by 2 to obtain the quotient (714).
1428 ÷ 2 = 714
• Step 3. Repeat step 1 with the obtained quotient (714).
714 ÷ 2 = 357
357 ÷ 3 = 119
119 ÷ 7 = 17
17 ÷ 17 = 1

So, the prime factorization of 1428 is, 1428 = 2 x 2 x 3 x 7 x 17.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1428 as shown below:

So, the prime factorization of 1428 is, 1428 = 2 x 2 x 3 x 7 x 17.

#### 3. Find factors of 1428 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 1428 would be the two numbers which, when multiplied, give 1428 as the result.

The following table represents the calculation of factors of 1428 in pairs:

Factor Pair Pair Factorization
1 and 1428 1 x 1428 = 1428
2 and 714 2 x 714 = 1428
3 and 476 3 x 476 = 1428
4 and 357 4 x 357 = 1428
6 and 238 6 x 238 = 1428
7 and 204 7 x 204 = 1428
12 and 119 12 x 119 = 1428
14 and 102 14 x 102 = 1428
17 and 84 17 x 84 = 1428
21 and 68 21 x 68 = 1428
28 and 51 28 x 51 = 1428
34 and 42 34 x 42 = 1428

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 1428. They are called negative pair factors.

Hence, the negative pairs of 1428 would be ( -1 , -1428 ) , ( -2 , -714 ) , ( -3 , -476 ) , ( -4 , -357 ) , ( -6 , -238 ) , ( -7 , -204 ) , ( -12 , -119 ) , ( -14 , -102 ) , ( -17 , -84 ) , ( -21 , -68 ) , ( -28 , -51 ) and ( -34 , -42 ) .

#### What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 1428 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 1428.
• Every number is a factor of zero (0), since 1428 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, 7, 12, 14, 17, 21, 28, 34, 42, 51, 68, 84, 102, 119, 204, 238, 357, 476, 714, 1428 are exact divisors of 1428.
• Factors of 1428 are 1, 2, 3, 4, 6, 7, 12, 14, 17, 21, 28, 34, 42, 51, 68, 84, 102, 119, 204, 238, 357, 476, 714, 1428. Each factor divides 1428 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 7, 12, 14, 17, 21, 28, 34, 42, 51, 68, 84, 102, 119, 204, 238, 357, 476, 714, 1428 are all less than or equal to 1428.

• How do you find factors of a negative number? ( eg. -1428 )?

Factors of -1428 are -1, -2, -3, -4, -6, -7, -12, -14, -17, -21, -28, -34, -42, -51, -68, -84, -102, -119, -204, -238, -357, -476, -714, -1428.

• What is the sum of all factors of 1428?

The sum of all factors of 1428 is 4032.

• What is prime factorization of 1428?

Prime factorization of 1428 is 2 x 2 x 3 x 7 x 17.

• What are the pair factors of 1428?

Pair factors of 1428 are (1,1428), (2,714), (3,476), (4,357), (6,238), (7,204), (12,119), (14,102), (17,84), (21,68), (28,51), (34,42).

• What are six multiples of 1428?

First five multiples of 1428 are 2856, 4284, 5712, 7140, 8568, 9996.

• Is 1428 a whole number?

Yes 1428 is a whole number.

• Which is the smallest prime factor of 1428?

Smallest prime factor of 1428 is 2.

• What are five multiples of 1428?

First five multiples of 1428 are 2856, 4284, 5712, 7140, 8568.

• Write all factors of 1428?

Factors of 1428 are 1, 2, 3, 4, 6, 7, 12, 14, 17, 21, 28, 34, 42, 51, 68, 84, 102, 119, 204, 238, 357, 476, 714, 1428.

#### Examples of Factors

Joey wants to write all the prime factors of 1428 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1428 are 2, 2, 3, 7, 17.
So in exponential form it can be written as 22 x 3 x 7 x 17.

How many factors are there for 1428?

Factors of 1428 are 1, 2, 3, 4, 6, 7, 12, 14, 17, 21, 28, 34, 42, 51, 68, 84, 102, 119, 204, 238, 357, 476, 714, 1428.
So there are in total 24 factors.

Kevin has been asked to write 23 factor(s) of 1428. Can you predict the answer?

23 factor(s) of 1428 are 1, 2, 3, 4, 6, 7, 12, 14, 17, 21, 28, 34, 42, 51, 68, 84, 102, 119, 204, 238, 357, 476, 714.

Sammy is puzzled while calculating the prime factors of 1428. Can you help him find them?

Factors of 1428 are 1, 2, 3, 4, 6, 7, 12, 14, 17, 21, 28, 34, 42, 51, 68, 84, 102, 119, 204, 238, 357, 476, 714, 1428.
Prime factors of 1428 are 2, 2, 3, 7, 17

What is prime factorization of 1428?

Prime factorization of 1428 is 2 x 2 x 3 x 7 x 17 = 22 x 3 x 7 x 17.

Ariel has been assigned the task to find the product of all the prime factors of 1428. Can you help her?

Prime factors of 1428 are 2, 2, 3, 7, 17.
Hence, the product of prime factors of 714.

Can you help Rubel to find out the product of the even factors of 1428?

Factors of 1428 are 1, 2, 3, 4, 6, 7, 12, 14, 17, 21, 28, 34, 42, 51, 68, 84, 102, 119, 204, 238, 357, 476, 714, 1428.
Even factors of 1428 are 2, 4, 6, 12, 14, 28, 34, 42, 68, 84, 102, 204, 238, 476, 714, 1428.
Hence, product of even factors of 1428 is; 2 x 4 x 6 x 12 x 14 x 28 x 34 x 42 x 68 x 84 x 102 x 204 x 238 x 476 x 714 x 1428 = 4.4265525551177676e+27.