# Factors of 1617

Factors of 1617 are 1, 3, 7, 11, 21, 33, 49, 77, 147, 231, 539, and 1617

#### How to find factors of a number

 1.   Find factors of 1617 using Division Method 2.   Find factors of 1617 using Prime Factorization 3.   Find factors of 1617 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 1617

• Divide 1617 by 1: 1617 ÷ 1 : Remainder = 0
• Divide 1617 by 3: 1617 ÷ 3 : Remainder = 0
• Divide 1617 by 7: 1617 ÷ 7 : Remainder = 0
• Divide 1617 by 11: 1617 ÷ 11 : Remainder = 0
• Divide 1617 by 21: 1617 ÷ 21 : Remainder = 0
• Divide 1617 by 33: 1617 ÷ 33 : Remainder = 0
• Divide 1617 by 49: 1617 ÷ 49 : Remainder = 0
• Divide 1617 by 77: 1617 ÷ 77 : Remainder = 0
• Divide 1617 by 147: 1617 ÷ 147 : Remainder = 0
• Divide 1617 by 231: 1617 ÷ 231 : Remainder = 0
• Divide 1617 by 539: 1617 ÷ 539 : Remainder = 0
• Divide 1617 by 1617: 1617 ÷ 1617 : Remainder = 0

Hence, Factors of 1617 are 1, 3, 7, 11, 21, 33, 49, 77, 147, 231, 539, and 1617

#### 2. Steps to find factors of 1617 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 1617 using the division method, follow these steps:

• Step 1. Start dividing 1617 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 1617, which is 3. Divide 1617 by 3 to obtain the quotient (539).
1617 ÷ 3 = 539
• Step 3. Repeat step 1 with the obtained quotient (539).
539 ÷ 7 = 77
77 ÷ 7 = 11
11 ÷ 11 = 1

So, the prime factorization of 1617 is, 1617 = 3 x 7 x 7 x 11.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1617 as shown below:

So, the prime factorization of 1617 is, 1617 = 3 x 7 x 7 x 11.

#### 3. Find factors of 1617 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 1617 would be the two numbers which, when multiplied, give 1617 as the result.

The following table represents the calculation of factors of 1617 in pairs:

Factor Pair Pair Factorization
1 and 1617 1 x 1617 = 1617
3 and 539 3 x 539 = 1617
7 and 231 7 x 231 = 1617
11 and 147 11 x 147 = 1617
21 and 77 21 x 77 = 1617
33 and 49 33 x 49 = 1617

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 1617. They are called negative pair factors.

Hence, the negative pairs of 1617 would be ( -1 , -1617 ) , ( -3 , -539 ) , ( -7 , -231 ) , ( -11 , -147 ) , ( -21 , -77 ) and ( -33 , -49 ) .

#### 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

• Every factor of a number is an exact divisor of that number, example 1, 3, 7, 11, 21, 33, 49, 77, 147, 231, 539, 1617 are exact divisors of 1617.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 1617 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 1617.

• How do you find factors of a negative number? ( eg. -1617 )?

Factors of -1617 are -1, -3, -7, -11, -21, -33, -49, -77, -147, -231, -539, -1617.

• What is the sum of all factors of 1617?

The sum of all factors of 1617 is 2736.

• What is prime factorization of 1617?

Prime factorization of 1617 is 3 x 7 x 7 x 11.

• What are the pair factors of 1617?

Pair factors of 1617 are (1,1617), (3,539), (7,231), (11,147), (21,77), (33,49).

• What are six multiples of 1617?

First five multiples of 1617 are 3234, 4851, 6468, 8085, 9702, 11319.

• Is 1617 a whole number?

Yes 1617 is a whole number.

• Which is the smallest prime factor of 1617?

Smallest prime factor of 1617 is 3.

• What are five multiples of 1617?

First five multiples of 1617 are 3234, 4851, 6468, 8085, 9702.

• Write all factors of 1617?

Factors of 1617 are 1, 3, 7, 11, 21, 33, 49, 77, 147, 231, 539, 1617.

#### Examples of Factors

Joey wants to write all the prime factors of 1617 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1617 are 3, 7, 7, 11.
So in exponential form it can be written as 3 x 72 x 11.

How many factors are there for 1617?

Factors of 1617 are 1, 3, 7, 11, 21, 33, 49, 77, 147, 231, 539, 1617.
So there are in total 12 factors.

Kevin has been asked to write 11 factor(s) of 1617. Can you predict the answer?

11 factor(s) of 1617 are 1, 3, 7, 11, 21, 33, 49, 77, 147, 231, 539.

Sammy is puzzled while calculating the prime factors of 1617. Can you help him find them?

Factors of 1617 are 1, 3, 7, 11, 21, 33, 49, 77, 147, 231, 539, 1617.
Prime factors of 1617 are 3, 7, 7, 11

What is prime factorization of 1617?

Prime factorization of 1617 is 3 x 7 x 7 x 11 = 3 x 72 x 11.

Ariel has been assigned the task to find the product of all the prime factors of 1617. Can you help her?

Prime factors of 1617 are 3, 7, 7, 11.
Hence, the product of prime factors of 231.

Can you help Rubel to find out the product of the even factors of 1617?

Factors of 1617 are 1, 3, 7, 11, 21, 33, 49, 77, 147, 231, 539, 1617.
Even factors of 1617 are 0.
Hence, product of even factors of 1617 is; 0 = 0.