13 × 1 to 13 × 20, the patterns inside the row, and how to learn it without chanting
The 13 times table runs 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, 156 — that is 13 × 1 up to 13 × 12. Extended to twenty it carries on 169, 182, 195, 208, 221, 234, 247, 260. Below is the full row written out, the patterns hiding inside it, the two or three facts that cause most of the trouble, and the fastest way to get the whole table to automatic recall.
13 × 1 = 13; 13 × 2 = 26; 13 × 3 = 39; 13 × 4 = 52; 13 × 5 = 65; 13 × 6 = 78; 13 × 7 = 91; 13 × 8 = 104; 13 × 9 = 117; 13 × 10 = 130; 13 × 11 = 143; 13 × 12 = 156.
Carried on past twelve: 13 × 13 = 169; 13 × 14 = 182; 13 × 15 = 195; 13 × 16 = 208; 13 × 17 = 221; 13 × 18 = 234; 13 × 19 = 247; 13 × 20 = 260.
Backwards is worth practising too, because division questions arrive in that direction: 156 ÷ 13 = 12; 143 ÷ 13 = 11; 130 ÷ 13 = 10; 117 ÷ 13 = 9; 104 ÷ 13 = 8; 91 ÷ 13 = 7.
Answers alternate odd, even, odd, even all the way up, because 13 is odd: 13, 26, 39, 52, 65, 78.
The last digits cycle: 3, 6, 9, 2, 5, 8, 1, 4, 7, 0, 3, 6. Once you notice the cycle you can rule out a wrong answer before you have finished working it out.
Above twelve, the easiest route is almost always to split the number: 13 × m is the same as 10 × m plus 3 × m. That turns an unfamiliar table into two you already know.
If the row still needs chanting from the beginning, the facts are recognised rather than recalled. Drill them shuffled, out of order, until any one of them can be answered on its own.
A useful test: ask for the answers in a random order and time each one. Anything that takes more than about two seconds is not yet learned, however well the row can be recited.
Start from the anchors. 13 × 1, 13 × 2, 13 × 5 and 13 × 10 come almost free — they are 13, 26, 65 and 130. Every other fact in the row is one short step from one of those four.
13 × 3 is 26 + 13 = 39. 13 × 4 is 26 doubled, which is 52. 13 × 6 is 65 + 13 = 78. 13 × 9 is 130 − 13 = 117. Building from anchors is far more reliable than counting up in thirteens from the start of the row.
Then drill in short bursts. Sixty seconds a day, shuffled, with the answers checked instantly, will beat a long weekly session every time — recall improves with the number of retrievals, not the number of minutes.
Times tables are not an end in themselves. They are the thing that makes longer arithmetic possible without a calculator: long multiplication, dividing, cancelling fractions, converting units, working out a percentage in your head. Each of those breaks down into table facts, so a slow table slows all of them down.
That is also why timing matters more than accuracy alone. A fact you can reach in half a second costs nothing inside a longer sum. A fact that takes four seconds costs four seconds every single time it appears.
The 13 times table is 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, 156, which is 13 × 1 through 13 × 12. Carried on to twenty it continues 169, 182, 195, 208, 221, 234, 247, 260.
13 × 7 = 91. A quick route is 13 × 5 = 65 plus 13 × 2 = 26, which adds to 91.
13 × 12 = 156. Split the twelve into 10 + 2: 130 + 26 = 156.
Learn the four anchors first — 13 × 1 = 13, 13 × 2 = 26, 13 × 5 = 65 and 13 × 10 = 130 — then build the rest by adding or subtracting one lot of 13. Drill the row shuffled for a minute a day rather than reciting it in order.
104 ÷ 13 = 8, because 13 × 8 = 104. Every fact in the table gives you a division fact for free.
Each fact in this row has a page of its own, and every table from 1 to 20 is listed on the times tables index.