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Factors of 69

69 is a special two-digit number that, besides 1 and 69, has only one other pair factor i.e. 3 and 23. In this lesson, we will calculate the factors of 69, prime factors of 69, and factors of 69 in pairs along with solved examples for a better understanding.

Factors of 69: 1, 3, 23 and 69
Prime Factorization of 69: 69 = 3 × 23

1.	What Are the Factors of 69?
2.	How to Calculate Factors of 69?
3.	Factors of 69 by Prime Factorization
4.	Factors of 69 in Pairs
5.	FAQs on Factors of 69

What are the Factors of 69?

A factor is a number that divides the given number equally without leaving a remainder. These numbers divide 69 equally.
The factors of 69 are 1, 3, 23, and 69.

How to Calculate the Factors of 69?

Let's learn to calculate the factors of 69 by division method. We know that the numbers which divide 69 without leaving remainder are its factors.

Let us divide 69 by 1. As 1 is a universal factor.
It divides any number, so 1 is a factor of 69.
69 ÷ 1 = 69
Therefore, 1 is a factor of 69.

We proceed with the next number 2. Since 69 is an odd number, it is not divisible by 2 and leaves a remainder. Let us divide by the next number which is 3.
69 ÷ 3 = 23
It leaves the remainder zero. Therefore, 3 is also a factor of 69.
69 ÷ 23 = 3

Note that 69 is odd, all of its factors will also be odd.

Therefore, the factors of 69 are 1, 3, 23 and 69.

Explore factors using illustrations and interactive examples

Factors of 62 - The factors of 62 are, 1, 2, 31, and 62
Factors of 63 - The factors of 63 are 1, 3, 7, 9, 21 and 63
Factors of 65 - The factors of 65 are 1, 5, 13, and 65
Factors of 66 - The factors of 66 are 1, 2, 3, 6, 11, 22, 33, and 66
Factors of 68 - The factors of 68 are 1, 2, 4, 17, 34, and 68
Factors of 169 - The factors of 169 are 1, 13, and 169

Factors of 69 by Prime Factorization

Prime factorization is a process of breaking down the composite number into the product of its prime factors. Since 69 is not an even number, it is not divisible by 2.
Now we start dividing 69 with the next least prime number. i.e, 3
69 ÷ 3 = 23

Since 23 is a prime number we stop the division here.

factors of 69 by upside down division

It can also be written as, 69 = 3 × 23

Think Tank:

Why is 69 called as semi-prime number?
9.6 × 10 = 96. Are 9.6 and 10 factors of 96? Think!

Factors of 69 in Pairs

The pair of numbers that give 69 when multiplied is called pair factors of 69. Here, the number 69 is obtained by:

1 × 69 = 69
3 × 23 = 69

Therefore, factors of 69 in pairs are (1, 69) and (3, 23).
Negative integers can also be its factors of 69 since their product gives 69. Therefore, negative pair factors of 69 are (-1, -69) and (-3, -23).

Important Notes:

Prime Factorization of 69 is 2 × 23.
Positive factors of 69 are 1, 3, 23, and 69.
Negative factors pair of 69 are (-1, -69) and (-3, -23).

Example 1: Sam has plucked 69 tomatoes from his garden. He wants it to be sold in three vegetable shops. Help Sam to sell an equal number of tomatoes in all three shops.

Solution:

There are 69 tomatoes in total. We know the factor pair of 69 is (3,23), so he can share 23 tomatoes to 3 shops each.
23 tomatoes × 3 shops = 69 tomatoes
Sam must sell 23 tomatoes to each shop.
Example 2: Can you help George to find the common factors of 69 and 81?

Solution:

Factors of 69 can be obtained by the following steps:

69 ÷ 1 = 69

1 × 69 = 69

We try with number 3.

69 ÷ 3 = 23

3 × 23 = 69

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

Factors of 81 can be obtained by following steps:

81 ÷ 1 = 81

1 × 81 = 81

We try with number 3.

81 ÷ 3 = 27

3 × 27 = 81

Numbers 5 and 7 are not factors of 81 since it is not dividing 81 equally.

We try with number 9.

81 ÷ 9 = 9

9 × 9 = 81

Continuing further we see that 27 divides 81 exactly and we already know that 3 × 27 = 81. Factors of 81 are 1, 3, 9, 27, and 81
Common factors of 69 and 81 are 1 and 3.
Example 3: Can you help Anna to find the common factors of 69 and 48?

Solution:

Let us list the factors of 69 and 48.
The factors of 60 are, 1, 3, 23, and 69.
The factors of 48 are, 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
Hence, the common factors of 60 and 48 are 1 and 3.

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FAQs on Factors of 69

What are the prime factors of 69?

Factors of 69 are 1, 3, 23, and 69.
Prime factors of 69 are 1, 3, 23.

What are the factors of 69 in pairs?

The pair of numbers that give 69 when multiplied is called pair factors of 69.
Therefore, factors of 69 in pairs are (1, 69) and (3, 23).
Negative integers can also be its factors of 69 since their product gives 69.
Therefore, negative pair factors of 69 are (-1, -69) and (-3, -23).

What are the factors of 69?

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

How many factors of 69 are perfect squares?

Factors of 69 are 1, 3, 23, and 69. There is no such factor of 69 which is a perfect square.

What are the common factors of 69 and 57?

The factors of 57 are 1, 3, 19, and 57
The factors of 69 are 1, 3, 23, and 69
1 and 3 are the common factor of 57 and 69.

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