Last Factor Loses

Players: 2 or more
Ages: 8 and up
Cost: Free!
Math Ideas: Multiplication, factors, prime and composite numbers
Questions to Ask
    Which numbers can't be factored any further?
    Let's play again with the same number and factor it differently. Who do you think will win?

This week's blog is jam packed!


I've got a brand-new video about my favorite board game ever, Blokus (more on that below)!

Not only that, I have two games to teach you this week! One is a fantastically fun road-trip game, and the second is its mathematical cousin.

I found both these games on the website of my friend John Golden, who is one of my favorite people to chat with about games and math. He is a math professor and a games addict, and his website is a cornucopia of awesome, mathy games.

Let's get into it! First up: Last Letter Loses!

How to Play: Last Letter Loses

This game, as I said, is perfect for a long car ride. Each player goes around, spelling the beginning of a word by adding a letter to its end. The goal of the game is to continue the spelling without ever actually spelling a word. If you add a letter that ends up spelling a word, you lose!

Here's what I mean. Let's say I am playing with a couple of other players:

Me: S

Thing One: S-P

Thing Two: S-P-R


So far, everyone is still in the game. We can all think of lots of words that begin with spr-, but nobody has spelled an actual word yet.  

(By the way, one, two, and three-letter words don't count in this game. So don't worry about spelling "car," but try to avoid spelling "cart"!)

Me: S - P - R - A

Thing One: S - P - R - A - N

Thing Two [with a sigh]: S - P - R - A - N - G

So Thing 2 loses this round. Play continues until only one player is left, and then you start a new game with everyone.

Note that if you are stuck you can always challenge the person just before you. That way, you ensure that everyone is always building toward a possible word. If you say "S - P - R - A - N - Z" and the next player challenges you, then you lose (unless you can think of a word that starts with spranz-).

Got it? Awesome! Now let's learn the mathematical cousin: Last Factor Loses

How to Play: Last Factor Loses


In this game, the first player names a number. The next player breaks down the number into two factors and lists them. 

The next player continues by taking one of those new numbers and breaking it down into two smaller factors. As with the previous game, the goal is to keep the factoring going, so that the next player can factor the number even further. The player who lists the most completely factored version of the number, loses. And no, you cannot use 1.

Here's an example.

Me: 48

Thing One: 4 * 12

Thing Two: 2 * 2 * 12

Me: 2 * 2 * 6 * 2

Thing One [with a sigh]: 2 * 2 * 3 * 2 * 2

In this case, the number cannot be factored any more, so Thing One is out. As with Last Letter Loses, play continues with a new number until one player is left standing.

Unlike Last Letter Loses, I think this game is probably best played on paper. That way, your kids don't have to keep track of every factor in their heads. Instead, they can see the list on paper and focus their thinking on finding new sets of numbers that work as factors for the existing set of numbers.

Where's the Math?

Last Factor Loses is a great way to get your kids to discover the power of prime numbers

Remember, prime numbers are those numbers that have only two factors: 1 and themselves. As a result, they are a sort of dead-end in this game. Once your opponent lists a prime number such as 3, you know that you can't factor it any further. All other numbers, such as 4, 12, and 15, can be factored further. These are known as composite numbers.

By the way, I'm not encouraging you to launch into a mini math lesson about prime numbers, necessarily. Your kids will start to see the distinction between primes and composites simply by playing the game repeatedly. Over time, they are likely to see that certain numbers, such as 2, 3, 5, and 7, tend to appear at the end of each round, while other numbers like 4, 6, and 9 are never listed. 

Playing this game is also a fantastic way to practice multiplication facts backwards. If you start with 24, your child has several options that they can use on their turn: 2 and 12, 4 and 3, or 6 and 2. Other starting numbers, such as 35, lead the opponent down a much more direct path...

Questions to Ask

After you've played a time or two, you might ask your child "Which numbers can't be factored any further?" They could even start a little list of those numbers off to the side of their paper as they play. 


Another fun follow-up is "What do you want to name these numbers that can't be broken down any further?" Yes, they already have a name, but it's fun to come up with your own sometimes!

Maybe your daughter wants to name them after herself, or her favorite pet, or maybe she wants to call them Diamond Numbers since they can't be shattered. Whatever she chooses will be memorable and fun, and the deep mathematical idea will transfer over when her 4th grade teacher introduces her to the vocabulary term prime numbers.

Once you've played a bunch, you could ask your child: "Let's play through that number again, but this time break it down differently. Who do you think will win?"

Perhaps your child will have an interesting intuition about how their choice of factors affects the outcome of the game. Perhaps you do as well! Seems like it would be worth testing to see if it plays out the way you expect...

My Latest Video

This week I'm excited to share a new video, all about Blokus! If you are a long-time reader of the newsletter, you'll know that Blokus is my all-time favorite board game, so I'm thrilled to finally share my passion for it in a video!

Free GamesKent HainesComment