Factors of 10 Using Prime Factorization
Factors of 10
The factors of 10 will be those numbers that divide the number 10 exactly and leave no remainder. We will learn how we can find the list of factors, prime factors and factor pairs of 10.
1. List of factors: To find out the total number of factors of 10, we need to do a divisibility test.
So, the factor list of 10 is: 1, 2, 5 and 10
2. Factor pairs:
The factor pairs of 10 are the pairs of factors whose multiplication is 10. The factor pairs of 10 are:
3. Prime factors of 10: The factor tree of 10 is
The prime factorization of 10 is: 2 \(\times\) 5
The prime factors of 10 can also be calculated through the following method:
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Rapid Recall
The factors of 10 are 1, 2, 5 and 10.
Solved Factors of 10 Examples
Example 1: Find the first 8 multiples of 10.
Solution:
When 10 is multiplied by natural numbers, the product is known as the multiples of 10. The first 8 multiples of 10 are:
10 \(\times\) 1 = 10
10 \(\times\) 2 = 20
10 \(\times\) 3 = 30
10 \(\times\) 4 = 40
10 \(\times\) 5 = 50
10 \(\times\) 6 = 60
10 \(\times\) 7 = 70
10 \(\times\) 8 = 80
Example 2: Use prime factorization to find the prime factors of 10 and then find the prime factors of 129.
Solution: The prime factors of 10 can be calculated as follows:
Therefore, 10 = 2 \(\times\) 5.
Similarly, the prime factors of 129 can be calculated as follows:
So, the prime factor of 129 are: 3 \(\times\) 43.
Example 3: Amy is an ace gymnast and she has won 10 medals in total. She wants to arrange these medals on her wall in the shape of rectangular arrays. How many different arrangements are possible?
Solution:
The arrangement is supposed to be done in a rectangular array form.
To find the number of ways in which we can arrange 10 medals in rectangular arrays, we can take the help of the factor pairs of 10.
The factor pairs of 10 are (1, 10) and (2, 5).
Therefore, Amy can arrange her medals in the following ways:
- 1 row of 10 medals or 1 column of 10 medals
- 2 rows and 5 columns or 5 rows and 2 columns
The positive factors pair of 10 are (1,1 0) and (5, 10)
The negative factors of 10 are (- 1, – 10) and (- 2, – 5)
The positive multiples of 10 are: 10 \(\times\) 1 = 10
10 \(\times\) 2 = 20
10 \(\times\) 3 = 30
10 \(\times\) 4 = 40
10 \(\times\) 5 = 50
The negative multiples of 10 are : 10 \(\times\) (- 1) = – 10
10 \(\times\) (- 2) = – 20
10 \(\times\) (- 3) = – 30
10 \(\times\) (- 4) = – 40
10 \(\times\) (- 5) = – 50
The prime factorization of 10 is: 1 \(\times\) 2 \(\times\) 5
10 has a factor other than 1 and itself, so it is not a prime number.
A number having more than two factors is called a composite number, so 10 is a composite number.
The factors of any number will be divisors that exactly divide the number, that is, they leave zero as the remainder.
The prime factor of a number is that factor that is also a prime number.
For example, the factors of 20 are 1, 2, 4, 5 and 10, and the prime factors of 20 are 2 and 5
1. No, because factors are the divisors of the number that leave 0 as the remainder. Hence, factors must be less than the number.
2. No. Since factors must be less than the number, the number of factors of any number is limited or finite.