Factors of 80 Using Prime Factorization
What are the Factors of 80?
The natural numbers that can divide a number evenly are known as the factors of that number. When 80 is divided by its factor, the remainder is zero, and the quotient is also a factor of 80.
Factor List of the Number 80
80 is a composite number, that is, it has more than two factors. The factors of 80 can be obtained using divisibility rules and division facts.
Therefore, the factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80.
The Prime Factors of 80
The factor tree below depicts the prime factorization of the number 80.
The prime factorization of 80 is 2 × 2 × 2 × 2 × 5 or \(2^4\) × 5. This means 2 and 5 are the prime factors of 80.
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The Positive Factor Pairs of 80
A factor pair of 80 is a set of two factors of 80, such that their product is 80. A number can have a positive pair of factors and a negative pair of factors.
For example, (1, 80) and (- 1, – 80) are the factor pairs of 80.
1 × 80 = 80
(- 1) × (- 80) = 80
[Note: The product of two negative numbers results in a positive number.]
Below is a list of positive factor pairs of 80.
Solved Factors of 80 Examples
Example 1: Find the common factors of 80 and 20.
Solution:
The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80.
The factors of 20 are 1, 2, 4, 5, 10, and 20.
Hence, the common factors of 80 and 20 are 1, 2, 4, 5, 10, and 20.
Example 2: Find the greatest common factor of 80 and 90.
Solution:
The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80.
The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.
The common factors of 80 and 90 are 1, 2, 5, and 10.
Hence, the greatest common factor of 80 and 90 is 10.
Example 3: Find the total number of common factors of 80 and 72.
Solution:
The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80.
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.
The common factors of 80 and 72 are 1, 2, 4, and 8.
Hence, 80 and 72 have 4 common factors in total.
Example 4: Jenny has 80 photos. She wants to arrange these photos evenly in a 20-page photo album. How many photos will she paste on each page of the album?
Solution:
Total number of photos = 80
Number of pages in the album = 20
To arrange the photos evenly in the album, divide the total number of photos by the number of pages in the album, that is, \(\frac{80}{20}\)
= \(\frac{20\times4}{20}\) [(20, 4) is a factor pair of 80]
= 4 [Divide both the numerator and the denominator by 20]
Therefore, Jenny will paste 4 photos on each page of the album.
A number having more than two factors is known as a composite number.
Any number will have at least two factors, that is, 1 and the number itself.
(- 1, – 80), (- 2, – 40), (- 4, – 20), (- 5, – 16), and (- 8, – 10) are the negative factor pairs of 80.
Yes, 16 is a factor of 80. This is because 16 divides 80 exactly and leaves the remainder 0.