- People on TikTok are stunned that 29 multiplied by 3 is 87.
- Number values can be very psychological, “sounding” one way while being another.
- Division rules and common core principles can help unwire psychology from math problems.
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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If you’re thinking your brain is way too smart to do such a simple math fallacy, we regret to inform you everyone has easily trickable human brains. Prices that “sound longer,” for example, are more discouraging to customers, even when we don’t say them aloud at any point. It gets worse: “For even murkier psychological reasons, using small fonts and physically putting your price on the left (of a webpage, say) may also nudge people toward thinking it’s relatively low,” Inc reports.
Let’s consider 87 with division rules. Sure, you’re not likely to find a division rule for 29. But the division rule for 3 would shake loose the right answer. You just add the digits of the number together, and if that sum is divisible by three, so is your whole number. 87 is 8 + 7, so 15, which is easily divisible by 3 and 5. When we pull the 3 out of 87, we get … 29.
Common core rules try to build similar rule sets in children’s minds so they’re not relying on how numbers “feel”—they have easy strategies to try to solve problems. In common core, you might divide 87 by 3 by taking away chunks of 30 to start with. So you have 60 + 27 instead of 87, and that leaves a smaller “feeling” problem to solve.
We understand why arithmetic that “feels” wrong is making people upset. Prime-sounding numbers are easy to assume things about, and 7 is one of the most popular lucky numbers around the world. Perhaps it’s, uh, prime time to review the division rules and look closer at some common core strategies.
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