#math trivia for #May4: #125 divides 1000. What other day-numbers divide a power of 10? What’s the general pattern these numbers follow?
— Burt Kaliski Jr. (@modulomathy) May 4, 2012
The day-numbers that divide a power of 10 (and the power they divide) are:
- 1 — 1
- 2 — 10
- 4 — 100
- 5 — 10
- 8 — 1000
- 10 — 10
- 16 — 10,000
- 20 — 100
- 25 — 100
- 32 — 100,000
- 40 — 1000
- 50 — 100
- 64 — 1,000,000
- 80 — 10,000
- 100 — 100
- 125 — 1000
- 128 — 10,000,000
- 160 — 100,000
- 200 — 1000
- 250 — 1000
- 256 — 100,000,000
- 320 — 1,000,000
The general pattern is a day-number divides a power of 10 if and only if it has the form 2^x * 5^y for x, y >= 0. The smallest power of 10 that the day-number divides is 10^z where z is the larger of x and y. If the day-number is divisible by any prime numbers other than 2 and 5, it cannot divide a power of 10, because powers of 10, being of the form 10^z = 2^z * 5^z, are only divisible by powers of 2, powers of 5, and their products.
