Factors of 219

2. Steps to find factors of 219 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 219 using the division method, follow these steps:

• Step 1. Start dividing 219 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 219, which is 3. Divide 219 by 3 to obtain the quotient (73).
  219 ÷ 3 = 73
• Step 3. Repeat step 1 with the obtained quotient (73).
  73 ÷ 73 = 1

So, the prime factorization of 219 is, 219 = 3 x 73.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 219 as shown below:

So, the prime factorization of 219 is, 219 = 3 x 73.

3. Find factors of 219 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 219 would be the two numbers which, when multiplied, give 219 as the result.

The following table represents the calculation of factors of 219 in pairs:

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 219. They are called negative pair factors.

Hence, the negative pairs of 219 would be ( -1 , -219 ) , ( -3 , -73 ) .

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 number is a factor of zero (0), since 219 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, 73, 219 are exact divisors of 219.
• Factors of 219 are 1, 3, 73, 219. Each factor divides 219 without leaving a remainder.

Frequently Asked Questions

• What are the prime factors of 219?

  The factors of 219 are 1, 3, 73, 219.
  Prime factors of 219 are 3, 73.

• What two numbers make 219?

  Two numbers that make 219 are 3 and 73.

• What is the greatest prime factors of 219?

  The greatest prime factor of 219 is 73.

• What are factors of 219?

  Factors of 219 are 1, 3, 73, 219.

• How do you find factors of a negative number? ( eg. -219 )?

  Factors of -219 are -1, -3, -73, -219.

• What are five multiples of 219?

  First five multiples of 219 are 438, 657, 876, 1095, 1314.

• Write some multiples of 219?

  First five multiples of 219 are 438, 657, 876, 1095.

• Is 219 a perfect square?

  No 219 is not a perfect square.

• What two numbers make 219?

  Two numbers that make 219 are 3 and 73.

Examples of Factors