Write 84 as a product of primes. Use index notation?

5 Answers

  • 12 x 7

    2^2 x 3 x 7

  • You can see 84 is divisible by 4, so 84 = 4*21

    84 = 2*2*3*7 = 2^2*3*7

  • 2^2 × 3 × 7

  • If you don’t know what prime numbers are, they are numbers that are only divisible by themselves and 1.

    These include: 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, etc.

    To write any number as a product of primes, you have to do a factor tree. Basically, you write the number and keep dividing it by prime numbers until you reach two prime numbers at the end.

    To show you, I’ll put all the prime numbers between ” “.

    ———————–

    Here’s the first step:

    84

    = “2” x 42

    Since 2 is prime number, it can’t be further simplified. Now, you’ll just have to divide 42 by another prime and another number, and repeat this until you can’t simplify anymore.

    So:

    84

    = “2” x 42

    42

    = “2” x 21

    21

    = “3” x “7”

    At this point, you’ve got two prime numbers: this is the end of the factorization. Now, take all the prime numbers

    ” “, and multiply them by each other. This gives you 84.

    2 x 2 x 3 x 7 = 84

    ———————

    Now, for the index notation part, you know how 2 x 2 is the same as 2^2? That’s all you have to do! Just represent any repeated numbers as exponents.

    84 = 2 x 2 x 3 x 7

    84 = 2^2 x 3 x 7

  • 84 = 7 x 12

    = 7 x 3 x 4

    = 7 x 3 x 2^2

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