# Factors of 272

Factors of 272 are 1, 2, 4, 8, 16, 17, 34, 68, 136, and 272

#### How to find factors of a number

 1.   Find factors of 272 using Division Method 2.   Find factors of 272 using Prime Factorization 3.   Find factors of 272 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 272

• Divide 272 by 1: 272 ÷ 1 : Remainder = 0
• Divide 272 by 2: 272 ÷ 2 : Remainder = 0
• Divide 272 by 4: 272 ÷ 4 : Remainder = 0
• Divide 272 by 8: 272 ÷ 8 : Remainder = 0
• Divide 272 by 16: 272 ÷ 16 : Remainder = 0
• Divide 272 by 17: 272 ÷ 17 : Remainder = 0
• Divide 272 by 34: 272 ÷ 34 : Remainder = 0
• Divide 272 by 68: 272 ÷ 68 : Remainder = 0
• Divide 272 by 136: 272 ÷ 136 : Remainder = 0
• Divide 272 by 272: 272 ÷ 272 : Remainder = 0

Hence, Factors of 272 are 1, 2, 4, 8, 16, 17, 34, 68, 136, and 272

#### 2. Steps to find factors of 272 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 272 using the division method, follow these steps:

• Step 1. Start dividing 272 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 272, which is 2. Divide 272 by 2 to obtain the quotient (136).
272 ÷ 2 = 136
• Step 3. Repeat step 1 with the obtained quotient (136).
136 ÷ 2 = 68
68 ÷ 2 = 34
34 ÷ 2 = 17
17 ÷ 17 = 1

So, the prime factorization of 272 is, 272 = 2 x 2 x 2 x 2 x 17.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 272 as shown below:

So, the prime factorization of 272 is, 272 = 2 x 2 x 2 x 2 x 17.

#### 3. Find factors of 272 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 272 would be the two numbers which, when multiplied, give 272 as the result.

The following table represents the calculation of factors of 272 in pairs:

Factor Pair Pair Factorization
1 and 272 1 x 272 = 272
2 and 136 2 x 136 = 272
4 and 68 4 x 68 = 272
8 and 34 8 x 34 = 272
16 and 17 16 x 17 = 272

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 272. They are called negative pair factors.

Hence, the negative pairs of 272 would be ( -1 , -272 ) , ( -2 , -136 ) , ( -4 , -68 ) , ( -8 , -34 ) and ( -16 , -17 ) .

#### How do you explain factors?

In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 272 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 272.
• Every number is a factor of zero (0), since 272 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, 4, 8, 16, 17, 34, 68, 136, 272 are exact divisors of 272.
• Factors of 272 are 1, 2, 4, 8, 16, 17, 34, 68, 136, 272. Each factor divides 272 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 8, 16, 17, 34, 68, 136, 272 are all less than or equal to 272.

• What two numbers make 272?

Two numbers that make 272 are 2 and 136.

• What is prime factorization of 272?

Prime factorization of 272 is 2 x 2 x 2 x 2 x 17.

• Write some multiples of 272?

First five multiples of 272 are 544, 816, 1088, 1360.

• Which is the smallest prime factor of 272?

The smallest prime factor of 272 is 2.

• Is 272 a perfect square?

No 272 is not a perfect square.

• What is the sum of all factors of 272?

The sum of all factors of 272 is 558.

• What are factors of 272?

Factors of 272 are 1, 2, 4, 8, 16, 17, 34, 68, 136, 272.

• How do you find factors of a negative number? ( eg. -272 )?

Factors of -272 are -1, -2, -4, -8, -16, -17, -34, -68, -136, -272.

• Is 272 a whole number?

Yes 272 is a whole number.

#### Examples of Factors

Joy wants to calculate mean of all the factors of 272. Help him in finding the mean of 272.

Factors of 272 are 1, 2, 4, 8, 16, 17, 34, 68, 136, 272.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 272 is 1 + 2 + 4 + 8 + 16 + 17 + 34 + 68 + 136 + 272 = 558.
Hence, the mean of factors of 272 is 558 ÷ 10 = 55.80.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 272? Help her in writing all the factors.

Positive factors are 1, 2, 4, 8, 16, 17, 34, 68, 136, 272.
Negative factors are -1, -2, -4, -8, -16, -17, -34, -68, -136, -272.

Joey wants to write all the prime factors of 272 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 272 are 2, 2, 2, 2, 17.
So in exponential form it can be written as 24 x 17.

Kevin has been asked to write 9 factor(s) of 272. Can you predict the answer?

9 factor(s) of 272 are 1, 2, 4, 8, 16, 17, 34, 68, 136.

Sammy is puzzled while calculating the prime factors of 272. Can you help him find them?

Factors of 272 are 1, 2, 4, 8, 16, 17, 34, 68, 136, 272.
Prime factors of 272 are 2, 2, 2, 2, 17

What is prime factorization of 272?

Prime factorization of 272 is 2 x 2 x 2 x 2 x 17 = 24 x 17.

Can you help Rubel to find out the product of the even factors of 272?

Factors of 272 are 1, 2, 4, 8, 16, 17, 34, 68, 136, 272.
Even factors of 272 are 2, 4, 8, 16, 34, 68, 136, 272.
Hence, product of even factors of 272 is; 2 x 4 x 8 x 16 x 34 x 68 x 136 x 272 = 87578116096.