Table of 21

How to say the table of 21

21 one is 21, 21 twos are 42, 21 threes are 63, 21 fours are 84, 21 fives are 105, 21 sixes are 126, 21 sevens are 147, 21 eights are 168, 21 nines are 189, 21 tens are 210.

A quick way to work it out

Twenty times plus once. For 21 × 6: 120 + 6 = 126. For 21 × 9: 180 + 9 = 189. Up to × 9 the units digit is simply the number you multiplied by.

Patterns in the table of 21

• Last digit. The last digits of the first ten answers are 1, 2, 3, 4, 5, 6, 7, 8, 9 and 0. Each digit from 0 to 9 appears exactly once, which happens only for numbers ending in 1, 3, 7 or 9. After × 10 the same order repeats.
• Odd and even. 21 is odd, so the answers go odd, even, odd, even: 21, 42, 63, 84, 105 and 126. An odd number times an odd number is odd, and times an even number is even.
• Digit totals. Add the digits of each answer until one digit is left, and you get 3, 6 and 9, repeating. Only 3, 6 and 9 appear, because 21 is a multiple of 3.
• Steps of 21. Each answer is 21 more than the one above it. So if 21 × 7 slips your mind, take 21 × 6 = 126 and add 21 to get 147.
• Total of the first ten. Add the first ten answers and you get 1155. That is 55 × 21, because 1 + 2 + 3 and so on up to 10 is 55.

How the table of 21 is built

21 is not prime: it can be written as 3 × 7. So its table can be built from a smaller one. For example 21 × 6 is 3 × 42, and 7 × 6 = 42, so the answer is 3 × 42 = 126. The square of 21 is 21 × 21 = 441. On a multiplication chart the squares lie on the diagonal line from top left to bottom right.

Split it. Above 10, the sure method is to split the number into tens and units. 21 × 8 is 20 × 8 plus 1 × 8, which is 160 + 8 = 168.

Where you meet 21

Three weeks are 21 days, because 21 = 3 × 7. So every answer in this table is also in the tables of 3 and 7.

Division facts from this table

Every line gives a division fact for free. From 21 × 7 = 147 you know that 147 ÷ 21 = 7 and 147 ÷ 7 = 21. To divide a number by 21, look for it in the answers above: 189 is on line 9, so 189 ÷ 21 = 9. More on this in division from tables.

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All tables: 1 to 10, 11 to 20, 21 to 30. Methods: table tricks.