Table of 19

How to say the table of 19

Nineteen one is 19, nineteen twos are 38, nineteen threes are 57, nineteen fours are 76, nineteen fives are 95, nineteen sixes are 114, nineteen sevens are 133, nineteen eights are 152, nineteen nines are 171, nineteen tens are 190.

In Hindi

उन्नीस एकम उन्नीस, उन्नीस दूनी अड़तीस, उन्नीस तिया सत्तावन, उन्नीस चौके छिहत्तर, उन्नीस पंजे पंचानवे, उन्नीस छक्के एक सौ चौदह, उन्नीस सत्ते एक सौ तैंतीस, उन्नीस अट्ठे एक सौ बावन, उन्नीस नवें एक सौ इकहत्तर, उन्नीस दहाई एक सौ नब्बे।

This is the traditional chant used in Hindi-medium schools. The words for the multiplier (एकम, दूनी, तिया and so on) vary a little from region to region. All the pahade from 2 to 20 are on the Hindi pahade page.

A quick way to work it out

Twenty times minus one lot. For 19 × 6: 120 − 6 = 114. In the first five rows there is a pattern to see: 19, 38, 57, 76, 95. The tens digit goes up by 2 each time and the units digit goes down by 1.

Patterns in the table of 19

• Last digit. The last digits of the first ten answers are 9, 8, 7, 6, 5, 4, 3, 2, 1 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. 19 is odd, so the answers go odd, even, odd, even: 19, 38, 57, 76, 95 and 114. 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. For the first nine answers you get 1, 2, 3, 4, 5, 6, 7, 8 and 9: every digit from 1 to 9, once each. This happens for every number that is not a multiple of 3.
• Steps of 19. Each answer is 19 more than the one above it. So if 19 × 7 slips your mind, take 19 × 6 = 114 and add 19 to get 133.
• Total of the first ten. Add the first ten answers and you get 1045. That is 55 × 19, because 1 + 2 + 3 and so on up to 10 is 55.

How the table of 19 is built

19 is a prime number: no smaller table contains it, apart from the table of 1. So 19 × 1 = 19 is the first time 19 shows up anywhere on a multiplication chart, and its table cannot be made by doubling or tripling a smaller one. The square of 19 is 19 × 19 = 361. 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. 19 × 8 is 10 × 8 plus 9 × 8, which is 80 + 72 = 152.

Where you meet 19

The number 19 is prime. It is one less than 20, which is why "twenty times minus once" is so handy for it, in the same way that 9 is handled from 10.

Division facts from this table

Every line gives a division fact for free. From 19 × 7 = 133 you know that 133 ÷ 19 = 7 and 133 ÷ 7 = 19. To divide a number by 19, look for it in the answers above: 171 is on line 9, so 171 ÷ 19 = 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.