# Factors of 1071

Factors of 1071 are 1, 3, 7, 9, 17, 21, 51, 63, 119, 153, 357, and 1071

#### How to find factors of a number

 1.   Find factors of 1071 using Division Method 2.   Find factors of 1071 using Prime Factorization 3.   Find factors of 1071 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 1071

• Divide 1071 by 1: 1071 ÷ 1 : Remainder = 0
• Divide 1071 by 3: 1071 ÷ 3 : Remainder = 0
• Divide 1071 by 7: 1071 ÷ 7 : Remainder = 0
• Divide 1071 by 9: 1071 ÷ 9 : Remainder = 0
• Divide 1071 by 17: 1071 ÷ 17 : Remainder = 0
• Divide 1071 by 21: 1071 ÷ 21 : Remainder = 0
• Divide 1071 by 51: 1071 ÷ 51 : Remainder = 0
• Divide 1071 by 63: 1071 ÷ 63 : Remainder = 0
• Divide 1071 by 119: 1071 ÷ 119 : Remainder = 0
• Divide 1071 by 153: 1071 ÷ 153 : Remainder = 0
• Divide 1071 by 357: 1071 ÷ 357 : Remainder = 0
• Divide 1071 by 1071: 1071 ÷ 1071 : Remainder = 0

Hence, Factors of 1071 are 1, 3, 7, 9, 17, 21, 51, 63, 119, 153, 357, and 1071

#### 2. Steps to find factors of 1071 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 1071 using the division method, follow these steps:

• Step 1. Start dividing 1071 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 1071, which is 3. Divide 1071 by 3 to obtain the quotient (357).
1071 ÷ 3 = 357
• Step 3. Repeat step 1 with the obtained quotient (357).
357 ÷ 3 = 119
119 ÷ 7 = 17
17 ÷ 17 = 1

So, the prime factorization of 1071 is, 1071 = 3 x 3 x 7 x 17.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1071 as shown below:

So, the prime factorization of 1071 is, 1071 = 3 x 3 x 7 x 17.

#### 3. Find factors of 1071 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 1071 would be the two numbers which, when multiplied, give 1071 as the result.

The following table represents the calculation of factors of 1071 in pairs:

Factor Pair Pair Factorization
1 and 1071 1 x 1071 = 1071
3 and 357 3 x 357 = 1071
7 and 153 7 x 153 = 1071
9 and 119 9 x 119 = 1071
17 and 63 17 x 63 = 1071
21 and 51 21 x 51 = 1071

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 1071. They are called negative pair factors.

Hence, the negative pairs of 1071 would be ( -1 , -1071 ) , ( -3 , -357 ) , ( -7 , -153 ) , ( -9 , -119 ) , ( -17 , -63 ) and ( -21 , -51 ) .

#### How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

#### Properties of factors

• Every number is a factor of zero (0), since 1071 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, 3, 7, 9, 17, 21, 51, 63, 119, 153, 357, 1071 are exact divisors of 1071.
• Factors of 1071 are 1, 3, 7, 9, 17, 21, 51, 63, 119, 153, 357, 1071. Each factor divides 1071 without leaving a remainder.

• Which is the smallest prime factor of 1071?

Smallest prime factor of 1071 is 3.

• Is 1071 a perfect square?

No 1071 is not a perfect square.

• What are five multiples of 1071?

First five multiples of 1071 are 2142, 3213, 4284, 5355, 6426.

• What is prime factorization of 1071?

Prime factorization of 1071 is 3 x 3 x 7 x 17.

• What are factors of 1071?

Factors of 1071 are 1, 3, 7, 9, 17, 21, 51, 63, 119, 153, 357, 1071.

• How do you find factors of a negative number? ( eg. -1071 )?

Factors of -1071 are -1, -3, -7, -9, -17, -21, -51, -63, -119, -153, -357, -1071.

• Is 1071 a whole number?

Yes 1071 is a whole number.

• Which is greatest factor of 1071?

The greatest factor of 1071 is 357.

• What are the prime factors of 1071?

The factors of 1071 are 1, 3, 7, 9, 17, 21, 51, 63, 119, 153, 357, 1071.
Prime factors of 1071 are 3, 3, 7, 17.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 1071. Can you help her?

Prime factors of 1071 are 3, 3, 7, 17.
Hence, the product of prime factors of 357.

Can you help Rubel to find out the product of the even factors of 1071?

Factors of 1071 are 1, 3, 7, 9, 17, 21, 51, 63, 119, 153, 357, 1071.
Even factors of 1071 are 0.
Hence, product of even factors of 1071 is; 0 = 0.

Joy wants to calculate mean of all the factors of 1071. Help him in finding the mean of 1071.

Factors of 1071 are 1, 3, 7, 9, 17, 21, 51, 63, 119, 153, 357, 1071.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 1071 is 1 + 3 + 7 + 9 + 17 + 21 + 51 + 63 + 119 + 153 + 357 + 1071 = 1872.
Hence, the mean of factors of 1071 is 1872 ÷ 12 = 156.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 1071? Help her in writing all the factors.

Positive factors are 1, 3, 7, 9, 17, 21, 51, 63, 119, 153, 357, 1071.
Negative factors are -1, -3, -7, -9, -17, -21, -51, -63, -119, -153, -357, -1071.

How many factors are there for 1071?

Factors of 1071 are 1, 3, 7, 9, 17, 21, 51, 63, 119, 153, 357, 1071.
So there are in total 12 factors.

Joey wants to write all the prime factors of 1071 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1071 are 3, 3, 7, 17.
So in exponential form it can be written as 32 x 7 x 17.

Kevin has been asked to write 11 factor(s) of 1071. Can you predict the answer?

11 factor(s) of 1071 are 1, 3, 7, 9, 17, 21, 51, 63, 119, 153, 357.