1. Steps to find factors of 169 using Division Method

Example: Find factors of 169

  • Divide 169 by 1: 169 ÷ 1 : Remainder = 0
  • Divide 169 by 13: 169 ÷ 13 : Remainder = 0
  • Divide 169 by 169: 169 ÷ 169 : Remainder = 0

Hence, Factors of 169 are 1, 13, and 169

2. Steps to find factors of 169 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 169 using the division method, follow these steps:

  • Step 1. Start dividing 169 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 169, which is 13. Divide 169 by 13 to obtain the quotient (13).
    169 ÷ 13 = 13
  • Step 3. Repeat step 1 with the obtained quotient (13).
    13 ÷ 13 = 1

So, the prime factorization of 169 is, 169 = 13 x 13.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 169 as shown below:

So, the prime factorization of 169 is, 169 = 13 x 13.

3. Find factors of 169 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 169 would be the two numbers which, when multiplied, give 169 as the result.

The following table represents the calculation of factors of 169 in pairs:

Factor Pair Pair Factorization
1 and 169 1 x 169 = 169
13 and 13 13 x 13 = 169

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 169. They are called negative pair factors.

Hence, the negative pairs of 169 would be ( -1 , -169 ) , ( -13 , -13 ) .

How can we define factors?

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

Properties of factors

  • Every factor of a number is an exact divisor of that number, example 1, 13, 169 are exact divisors of 169.
  • Every number other than 1 has at least two factors, namely the number itself and 1.
  • Each number is a factor of itself. Eg. 169 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 169.

Frequently Asked Questions

  • Which is the smallest prime factor of 169?

    The smallest prime factor of 169 is 13.

  • Is 169 a whole number?

    Yes 169 is a whole number.

  • What are the prime factors of 169?

    The factors of 169 are 1, 13, 169.
    Prime factors of 169 are 13, 13.

  • What two numbers make 169?

    Two numbers that make 169 are 13 and 13.

  • What are multiples of 169?

    First five multiples of 169 are 338, 507, 676, 845.

  • What is the sum of all factors of 169?

    The sum of all factors of 169 is 183.

  • What are five multiples of 169?

    First five multiples of 169 are 338, 507, 676, 845, 1014.

  • Is 169 a perfect square?

    Yes 169 is a perfect square.

  • What is the greatest prime factors of 169?

    The greatest prime factor of 169 is 13.

Examples of Factors

How many factors are there for 169?

Factors of 169 are 1, 13, 169.
So there are in total 3 factors.

Kevin has been asked to write 2 factor(s) of 169. Can you predict the answer?

2 factor(s) of 169 are 1, 13.

Sammy is puzzled while calculating the prime factors of 169. Can you help him find them?

Factors of 169 are 1, 13, 169.
Prime factors of 169 are 13, 13

What is prime factorization of 169?

Prime factorization of 169 is 13 x 13 = 132.

Ariel has been assigned the task to find the product of all the prime factors of 169. Can you help her?

Prime factors of 169 are 13, 13.
Hence, the product of prime factors of 13.

Can you help Rubel to find out the product of the even factors of 169?

Factors of 169 are 1, 13, 169.
Even factors of 169 are 0.
Hence, product of even factors of 169 is; 0 = 0.

Joy wants to calculate mean of all the factors of 169. Help him in finding the mean of 169.

Factors of 169 are 1, 13, 169.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 169 is 1 + 13 + 169 = 183.
Hence, the mean of factors of 169 is 183 ÷ 3 = 61.00.