Factors & Prime Numbers
"Go into a Bigger Number"
Factors are numbers that divide evenly into a larger number. This video introduces the concept of factors and guides students through the factorization process. The song explains that all numbers have 1 and themselves as factors and that prime numbers have only these two factors.
F A C T O R S
We’re the factors.
We go into a bigger number evenly,
Yeah, don’t get it backwards. (x2)
Factors go into a bigger number evenly,
With nothing left over, believe in me.
Memorize your times table like an actor,
All numbers have 1 as a factor.
'Cause all numbers can be divided by 1,
With no remainder, that’s how it’s done.
If you have a number and you need to know
All its factors, just start the show.
We figure out our factors by closing the curtain,
Let’s try 32, see how it’s working.
The first combo we can multiply to get 32
Is 1 and 32.
Write the 1 on the left, 32 over there,
Now we try 2, to find the next pair.
2 goes into 32 sixteen times,
So we write the 16 on the right–hand side.
Next up is 3, well let’s see,
Does 3 go into 32? Not evenly.
So it’s not a factor, but what about 4?
That goes in 8 times, yeah for sure.
5, 6 or 7? They don’t go,
And now you can see that the curtain is closed.
That’s all the factors for 32, for sure!
Now hit the spotlight, for the next show.
If a number only has two factors,
Itself and the number 1, then the fact is
We call that number prime,
Like Optimus Prime, they’re one of a kind.
3 is prime, so are 5 and 7,
9’s not prime, but there’s prime at 11.
101, that’s certainly prime,
So is 3559.
F A C T O R S
We’re the factors.
We go into a bigger number evenly,
Yeah, don’t get it backwards. (x2)
A factor is a number that divides evenly into another number, without a remainder left over. So since 2 can be divided into 6, it is a factor of 6. So are 1, 3 and 6.
A factor is a number that divides evenly into another number, without a remainder left over. So since 2 can be divided into 6, it is a factor of 6. So are 1, 3 and 6.
All numbers have 1 as a factor, since all numbers are divisible by 1. When you divide a number by 1, you get the same number you started with.
All numbers have 1 as a factor, since all numbers are divisible by 1. When you divide a number by 1, you get the same number you started with.
The easiest way to make sure you list all of the factors of a number is to start dividing smaller numbers into it. Start with the number 1 and work your way up. Write the smaller factors on the left side of the page, in order, and write the bigger factors on the right. You know you have them all when you reach the middle number. Picture a curtain on a stage closing in from the right and left. You want to factor until the curtain is closed. Here is how we factor 32:
1 ... 32
1, 2 ... 16, 32
We try 3, but we see that it isn't a factor.
1, 2, 4 ... 8, 16, 32
We try 5, 6 and 7, but we see that they aren't factors. Should we try 8? We already know it's a factor, because we listed it when we divided 32 by 4. The curtain is now closed and we have all our factors for 32: 1, 2, 4, 8, 16, 32
The easiest way to make sure you list all of the factors of a number is to start dividing smaller numbers into it. Start with the number 1 and work your way up. Write the smaller factors on the left side of the page, in order, and write the bigger factors on the right. You know you have them all when you reach the middle number. Picture a curtain on a stage closing in from the right and left. You want to factor until the curtain is closed. Here is how we factor 32:
1 ... 32
1, 2 ... 16, 32
We try 3, but we see that it isn't a factor.
1, 2, 4 ... 8, 16, 32
We try 5, 6 and 7, but we see that they aren't factors. Should we try 8? We already know it's a factor, because we listed it when we divided 32 by 4. The curtain is now closed and we have all our factors for 32: 1, 2, 4, 8, 16, 32
Let’s try it with another number: 36.
1 and 36
2 and 18
3 and 13
4 and 9
6 (and 6)
Or: 1, 2, 3, 4, 6, 9, 13, 18, 36
That’s a lot of factors!
1 and 36
2 and 18
3 and 13
4 and 9
6 (and 6)
Or: 1, 2, 3, 4, 6, 9, 13, 18, 36
That’s a lot of factors!
All numbers have 1 and themselves as factors, and with prime numbers, those are the only two factors they have. 3 is a prime number because its only factors are 1 and 3, but 4 is not a prime number because it also has 2 as a factor.
All numbers have 1 and themselves as factors, and with prime numbers, those are the only two factors they have. 3 is a prime number because its only factors are 1 and 3, but 4 is not a prime number because it also has 2 as a factor.
There are some really big prime numbers out there. In 300 BC, the Greek mathematician Euclid proved that there are actually infinite prime numbers. The largest known prime number has 12,978,189 digits! And mathematicians (and computers) are on the lookout for even bigger ones.
There are some really big prime numbers out there. In 300 BC, the Greek mathematician Euclid proved that there are actually infinite prime numbers. The largest known prime number has 12,978,189 digits! And mathematicians (and computers) are on the lookout for even bigger ones.
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