We posted a math fact last week about the prime numbers 2 and 5.
Last Monday's math fact: 2 and 5 are the only prime numbers that end with a 2 or a 5.
We received a few requests to explain this math fact.
How is it possible that 2 and 5 are the only prime numbers that end with a 2 or a 5?
We need to know a few facts to understand how this is possible.
First, we need to know what is a prime number.
What is a prime number??
A prime number is a number greater than one that only has one and itself as a factor.
A few prime numbers are 2,3,5,7,11,13,17,19 and 23.
The numbers listed above have only two factors, which are one and itself.
Example 1
The factors of the number 3 are 1 and 3.
Second, we need to know the definition of a factor.
What is a factor?
A factor is a number that can be multiplied or divided to produce a certain number.
Example 2
Let's look at the number 10.
1x10=10
2x5=10
10÷2=5
10÷5=2
10÷1=10
10÷10=1
1,2,5, and 10 are factors of 10.
Third, we need to know the definition of a multiple.
What is a multiple?
A multiple is a number produced when a number is multiplied by an integer.
Example 3
Let's look at the number 10 again.
10x1=10
10x2=20
10x3=30
10x4=40
The numbers 10, 20, 30, and 40 are considered multiples of 10.
Fourth, we need to know facts about the number 2.
Number 2 facts
The number 2 only has two factors, 1 and 2, which makes it a prime number.
Two is a factor of any number ending in 2.
Any number ending in 2 is a multiple of 2.
Any other number ending in two other than two has more than two factors.
Below is a list of some of the numbers that end in 2.
12,22,32,42,52,62,72,82 and 92.
All these numbers listed above have more than two factors.
Example 4
Let us look at the number 22.
The number 22 has four factors: 1,2,11 and 22.
1x22=22
2x11=22
Fifth, we need to know facts about the number 5.
Number 5 facts
The number 5 only has two factors, 1 and 5, which makes it a prime number.
Five is a factor of any number ending in 5.
Any number ending in 5 is a multiple of 5.
Any numbers ending in five other than five have more than two factors.
Below is a list ofsome of the numbers that end in 5:
15,25,35,45,55,65,75,85 and 95.
Example 5
Let us look at number 15.
The number 15 has four factors: 1,3,5 and 15.
1x15=15
3x5=15
2 and 5 are the only prime numbers that end with a 2 or a 5 because:
Prime numbers only have two factors.
Any numbers ending in 2 other than 2 have more than two factors.
Any numbers ending in 5 other than 5 have more than two factors.
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