On dividing a natural number by 13, the remainder is 3 and on dividing the same number by 21, the remainder is 11. Ifthe number lies between 500 and 600, then the remainder on dividing the number by 19 is

9514 1404 393

  4

Step-by-step explanation:

The least common multiple of 13 and 21 is 274, so the number of interest will be 10 less than that. The value in the given range is ...

  2(274) -10 = 536

We are interested in the remainder from 536/19, which is 4.

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536 = 13·41 +3 = 21·25 +11 = 19·28 +4

6mm^3 or .6cm^3

      216

      /   \

  36     6

  /   \     /

6     6   6

factor trees are nice.

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis: