# Factors of 1050

Factors of 1050 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 25, 30, 35, 42, 50, 70, 75, 105, 150, 175, 210, 350, 525, and 1050

#### How to find factors of a number

 1.   Find factors of 1050 using Division Method 2.   Find factors of 1050 using Prime Factorization 3.   Find factors of 1050 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 1050

• Divide 1050 by 1: 1050 ÷ 1 : Remainder = 0
• Divide 1050 by 2: 1050 ÷ 2 : Remainder = 0
• Divide 1050 by 3: 1050 ÷ 3 : Remainder = 0
• Divide 1050 by 5: 1050 ÷ 5 : Remainder = 0
• Divide 1050 by 6: 1050 ÷ 6 : Remainder = 0
• Divide 1050 by 7: 1050 ÷ 7 : Remainder = 0
• Divide 1050 by 10: 1050 ÷ 10 : Remainder = 0
• Divide 1050 by 14: 1050 ÷ 14 : Remainder = 0
• Divide 1050 by 15: 1050 ÷ 15 : Remainder = 0
• Divide 1050 by 21: 1050 ÷ 21 : Remainder = 0
• Divide 1050 by 25: 1050 ÷ 25 : Remainder = 0
• Divide 1050 by 30: 1050 ÷ 30 : Remainder = 0
• Divide 1050 by 35: 1050 ÷ 35 : Remainder = 0
• Divide 1050 by 42: 1050 ÷ 42 : Remainder = 0
• Divide 1050 by 50: 1050 ÷ 50 : Remainder = 0
• Divide 1050 by 70: 1050 ÷ 70 : Remainder = 0
• Divide 1050 by 75: 1050 ÷ 75 : Remainder = 0
• Divide 1050 by 105: 1050 ÷ 105 : Remainder = 0
• Divide 1050 by 150: 1050 ÷ 150 : Remainder = 0
• Divide 1050 by 175: 1050 ÷ 175 : Remainder = 0
• Divide 1050 by 210: 1050 ÷ 210 : Remainder = 0
• Divide 1050 by 350: 1050 ÷ 350 : Remainder = 0
• Divide 1050 by 525: 1050 ÷ 525 : Remainder = 0
• Divide 1050 by 1050: 1050 ÷ 1050 : Remainder = 0

Hence, Factors of 1050 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 25, 30, 35, 42, 50, 70, 75, 105, 150, 175, 210, 350, 525, and 1050

#### 2. Steps to find factors of 1050 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 1050 using the division method, follow these steps:

• Step 1. Start dividing 1050 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 1050, which is 2. Divide 1050 by 2 to obtain the quotient (525).
1050 ÷ 2 = 525
• Step 3. Repeat step 1 with the obtained quotient (525).
525 ÷ 3 = 175
175 ÷ 5 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1

So, the prime factorization of 1050 is, 1050 = 2 x 3 x 5 x 5 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1050 as shown below:

So, the prime factorization of 1050 is, 1050 = 2 x 3 x 5 x 5 x 7.

#### 3. Find factors of 1050 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 1050 would be the two numbers which, when multiplied, give 1050 as the result.

The following table represents the calculation of factors of 1050 in pairs:

Factor Pair Pair Factorization
1 and 1050 1 x 1050 = 1050
2 and 525 2 x 525 = 1050
3 and 350 3 x 350 = 1050
5 and 210 5 x 210 = 1050
6 and 175 6 x 175 = 1050
7 and 150 7 x 150 = 1050
10 and 105 10 x 105 = 1050
14 and 75 14 x 75 = 1050
15 and 70 15 x 70 = 1050
21 and 50 21 x 50 = 1050
25 and 42 25 x 42 = 1050
30 and 35 30 x 35 = 1050

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 1050. They are called negative pair factors.

Hence, the negative pairs of 1050 would be ( -1 , -1050 ) , ( -2 , -525 ) , ( -3 , -350 ) , ( -5 , -210 ) , ( -6 , -175 ) , ( -7 , -150 ) , ( -10 , -105 ) , ( -14 , -75 ) , ( -15 , -70 ) , ( -21 , -50 ) , ( -25 , -42 ) and ( -30 , -35 ) .

#### What are factors?

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

#### Properties of factors

• Each number is a factor of itself. Eg. 1050 is a factor of itself.
• 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, 5, 6, 7, 10, 14, 15, 21, 25, 30, 35, 42, 50, 70, 75, 105, 150, 175, 210, 350, 525, 1050 are exact divisors of 1050.
• 1 is a factor of every number. Eg. 1 is a factor of 1050.
• Every number is a factor of zero (0), since 1050 x 0 = 0.

• How do you find factors of a negative number? ( eg. -1050 )?

Factors of -1050 are -1, -2, -3, -5, -6, -7, -10, -14, -15, -21, -25, -30, -35, -42, -50, -70, -75, -105, -150, -175, -210, -350, -525, -1050.

• What is the sum of all factors of 1050?

The sum of all factors of 1050 is 2976.

• What is prime factorization of 1050?

Prime factorization of 1050 is 2 x 3 x 5 x 5 x 7.

• What are the pair factors of 1050?

Pair factors of 1050 are (1,1050), (2,525), (3,350), (5,210), (6,175), (7,150), (10,105), (14,75), (15,70), (21,50), (25,42), (30,35).

• What are six multiples of 1050?

First five multiples of 1050 are 2100, 3150, 4200, 5250, 6300, 7350.

• Is 1050 a whole number?

Yes 1050 is a whole number.

• Which is the smallest prime factor of 1050?

Smallest prime factor of 1050 is 2.

• What are five multiples of 1050?

First five multiples of 1050 are 2100, 3150, 4200, 5250, 6300.

• Write all factors of 1050?

Factors of 1050 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 25, 30, 35, 42, 50, 70, 75, 105, 150, 175, 210, 350, 525, 1050.

#### Examples of Factors

Joey wants to write all the prime factors of 1050 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1050 are 2, 3, 5, 5, 7.
So in exponential form it can be written as 2 x 3 x 52 x 7.

How many factors are there for 1050?

Factors of 1050 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 25, 30, 35, 42, 50, 70, 75, 105, 150, 175, 210, 350, 525, 1050.
So there are in total 24 factors.

Kevin has been asked to write 23 factor(s) of 1050. Can you predict the answer?

23 factor(s) of 1050 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 25, 30, 35, 42, 50, 70, 75, 105, 150, 175, 210, 350, 525.

Sammy is puzzled while calculating the prime factors of 1050. Can you help him find them?

Factors of 1050 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 25, 30, 35, 42, 50, 70, 75, 105, 150, 175, 210, 350, 525, 1050.
Prime factors of 1050 are 2, 3, 5, 5, 7

What is prime factorization of 1050?

Prime factorization of 1050 is 2 x 3 x 5 x 5 x 7 = 2 x 3 x 52 x 7.

Ariel has been assigned the task to find the product of all the prime factors of 1050. Can you help her?

Prime factors of 1050 are 2, 3, 5, 5, 7.
Hence, the product of prime factors of 210.

Can you help Rubel to find out the product of the even factors of 1050?

Factors of 1050 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 25, 30, 35, 42, 50, 70, 75, 105, 150, 175, 210, 350, 525, 1050.
Even factors of 1050 are 2, 6, 10, 14, 30, 42, 50, 70, 150, 210, 350, 1050.
Hence, product of even factors of 1050 is; 2 x 6 x 10 x 14 x 30 x 42 x 50 x 70 x 150 x 210 x 350 x 1050 = 85766121000000000000.