If 2020 was the year of 2 + 2 = 5, maybe 2021 will be the year of … prime factorization? Right now, TikTok users are freaking out about the number 87, which surprisingly divides cleanly by 29. (The answer is 3!)

The realization has even driven some people to tears:

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This reaction is obviously exaggerated for humor—please, don’t actually let math make you cry—but the size of this internet ripple tells us something about how people think of numbers. Why is this simple problem surprising, and what does it say about how numbers “feel” when they go together?

Many people probably don’t know what factoring is, so let’s define our terms. There are two kinds of numbers: primes and compounds. Primes are divisible only by 1 and themselves, like 3, 13, 23, and 43. Compound numbers like 33, meanwhile, are divisible by more values, such as 1, 3, 11, 33.

There’s an easy way to factor most small numbers. For divisors 2 through 11, there are division rules that make it easy to divide them at a glance—or you could just start dividing on paper. So a number like 64 quickly becomes 2 x 32, 2 x 2 x 16, and so on. 12323212 becomes 11 x 1120292 becomes 11 x 2 x 560146, 11 x 2 x 2 x 280073, and so on.

But 29 x 3 = 87 registers as strange to people. Why is that? It’s not about factoring. Instead, it’s something about how numbers seem or even “feel” to us.

The number 7, for example, is __one of the most popular numbers__ around the world, from its use in gambling to its inherent luckiness. But it’s also odd and prime, so it’s easy to see why a number that ends with 7 *feels* like it doesn’t divide easily.

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