Every once in a while, a simple-looking equation pops up and suddenly your entire comments section becomes a battlefield of confident answers.
Today’s brain-teaser is:
21 ÷ 7 × 2!
Looks easy, right?
That’s exactly why people get it wrong.
When factorials appear, many people switch into “fast math” mode and forget how order of operations actually works. So let’s walk through the three most common answers people usually give—plus what’s really going on.
💭 Possible Answer #1: “It’s 6!”
This answer happens when someone solves it from left to right without noticing the factorial:
21 ÷ 7 = 3
3 × 2 = 6
The mistake?
They treated 2! as 2, not as the factorial of 2.
💭 Possible Answer #2: “It’s 42!”
This usually happens when someone sees the factorial and panics (just a little). They jump to:
2! = 2
21 × 2 = 42
Then they divide or forget to divide at all.
This skips the left-to-right rule for division and multiplication.
💭 Possible Answer #3: “It’s 3!”
Some do the factorial correctly, but they jump ahead in the steps:
2! = 2
21 ÷ (7 × 2) = 21 ÷ 14 = 1.5
Rounded or mistaken as 3, depending on how they group it.
The issue:
Adding parentheses that aren’t actually there.
✅ The Correct Answer
Let’s solve it properly using PEMDAS/BODMAS:
Step 1 — Factorial first
2! = 2
Now the equation is:
21 ÷ 7 × 2
Step 2 — Division & multiplication (left to right)
21 ÷ 7 = 3
3 × 2 = 6
🎉 Final Answer: 6
Another perfect example of how a simple factorial can completely change how people process an equation.
