Factors of 69

2. Steps to find factors of 69 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 69 using the division method, follow these steps:

• Step 1. Start dividing 69 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 69, which is 3. Divide 69 by 3 to obtain the quotient (23).
  69 ÷ 3 = 23
• Step 3. Repeat step 1 with the obtained quotient (23).
  23 ÷ 23 = 1

So, the prime factorization of 69 is, 69 = 3 x 23.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 69 as shown below:

So, the prime factorization of 69 is, 69 = 3 x 23.

3. Find factors of 69 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 69 would be the two numbers which, when multiplied, give 69 as the result.

The following table represents the calculation of factors of 69 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 69. They are called negative pair factors.

Hence, the negative pairs of 69 would be ( -1 , -69 ) , ( -3 , -23 ) .

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, 3, 23, 69 are exact divisors of 69.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 69 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 69.

Frequently Asked Questions

• How do you find factors of a negative number? ( eg. -69 )?

  Factors of -69 are -1, -3, -23, -69.

• What is the sum of all factors of 69?

  The sum of all factors of 69 is 96.

• What is prime factorization of 69?

  Prime factorization of 69 is 3 x 23.

• What are the pair factors of 69?

  Pair factors of 69 are (1,69), (3,23).

• What are six multiples of 69?

  First five multiples of 69 are 138, 207, 276, 345, 414, 483.

• Is 69 a whole number?

  Yes 69 is a whole number.

• Which is the smallest prime factor of 69?

  Smallest prime factor of 69 is 3.

• What are five multiples of 69?

  First five multiples of 69 are 138, 207, 276, 345, 414.

• Write all factors of 69?

  Factors of 69 are 1, 3, 23, 69.

Examples of Factors