Table of 3

How to say the table of 3

Three one is 3, three twos are 6, three threes are 9, three fours are 12, three fives are 15, three sixes are 18, three sevens are 21, three eights are 24, three nines are 27, three tens are 30.

In Hindi

तीन एकम तीन, तीन दूनी छह, तीन तिया नौ, तीन चौके बारह, तीन पंजे पंद्रह, तीन छक्के अठारह, तीन सत्ते इक्कीस, तीन अट्ठे चौबीस, तीन नवें सत्ताईस, तीन दहाई तीस।

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

Double, then add once more. For 3 × 8, double 8 to get 16 and add another 8 to reach 24. For 3 × 15, think 30 + 15 = 45. Check any answer by adding its digits: for a multiple of 3 the digit total is always 3, 6 or 9 (27 gives 2 + 7 = 9).

Patterns in the table of 3

• Last digit. The last digits of the first ten answers are 3, 6, 9, 2, 5, 8, 1, 4, 7 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. 3 is odd, so the answers go odd, even, odd, even: 3, 6, 9, 12, 15 and 18. 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 3 is a multiple of 3.
• Steps of 3. Each answer is 3 more than the one above it. So if 3 × 7 slips your mind, take 3 × 6 = 18 and add 3 to get 21.
• Total of the first ten. Add the first ten answers and you get 165. That is 55 × 3, because 1 + 2 + 3 and so on up to 10 is 55.

How the table of 3 is built

3 is a prime number: no smaller table contains it, apart from the table of 1. So 3 × 1 = 3 is the first time 3 shows up anywhere on a multiplication chart, and its table cannot be made by doubling or tripling a smaller one. The square of 3 is 3 × 3 = 9. On a multiplication chart the squares lie on the diagonal line from top left to bottom right.

How much is really new? Because 3 × 3 is the same as 3 × 3, a child who already knows the tables below 3 has met most of this one. Up to × 10, only 8 facts are new: 3 × 3, 3 × 4, 3 × 5, 3 × 6, 3 × 7, 3 × 8, 3 × 9 and 3 × 10.

Where you meet 3

Triangles have 3 sides, an auto rickshaw has 3 wheels, and a hat-trick is 3 in a row. Seven auto rickshaws have 3 × 7 = 21 wheels. The digit-total check is the same rule that tells you whether a big number divides by 3.

Division facts from this table

Every line gives a division fact for free. From 3 × 7 = 21 you know that 21 ÷ 3 = 7 and 21 ÷ 7 = 3. To divide a number by 3, look for it in the answers above: 27 is on line 9, so 27 ÷ 3 = 9. More on this in division from tables.

Try these

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Next

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