1000 x 4 = 4000
1000 times 4 is 4000. Because 4 is two doublings, the quickest mental route is 1000 to 2000 to 4000, with no column arithmetic at any point. The chain and the checks are below.
1,000 × 4 = 4,000
Adding 1,000 to itself 4 times gives the same answer.
Double it twice
4 is 2 x 2, so multiplying by 4 is doubling twice. 1000 doubled is 2000; 2000 doubled is 4000. Nothing to carry and nothing to line up. The zero rule arrives at the same place just as fast: multiplying by 1000 puts three zeros after the 4.
The doubling chain
- 1000
- 1000 x 2 = 2000
- 1000 x 4 = 4000
- 1000 x 8 = 8000
- 1000 x 16 = 16000
Each line is the one above it doubled. This shortcut exists because 4 is a power of two; it does not help with 1000 x 3, where there is no way round adding a third thousand.
The factors of 4000
4000 is 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 — five 2s and three 5s, and nothing else. Those group neatly into 32 x 125 = 4000. It is not divisible by 3, by 7 or by 9.
The same answer from elsewhere
40 x 100 is also 4000, using the same three zeros in a different arrangement. And 4 metres is 4000 millimetres, which is this multiplication doing a unit conversion under another name. The full set is on the multiplication answers page.