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WHAT IS THE PRIME FACTORIZATION OF 45? and what is the sum of the only two prime numbers that differ by one ? Thank you

  • math -

    45 = 3^2 5^1

    2+3 = 5

  • math -

    Thank you , but could you explain the factorization of 45? Idont get it

  • math -

    The easiest way to find the factors is to start with the smallest prime, and see whether it is a factor. Continue dividing successive primes until all you are left with is 1.

    Is 2 a factor of 45? No.

    How about he next prime (3)?
    3 divides 45 twice, so 3^2 is included in the list.
    45/3^2 = 5, so we keep going.

    5 divides 5 once, so 5^1 is in the list.
    5/5 = 1, so we are done.

    The list of factors is 3^2 5^1

    Consider 166600

    166600/2 = 83300
    83300/2 = 41650
    41650/2 = 20825
    2 does not divide 20825, so 2^3 is in the list

    3 does not divide 20825

    20825/5 = 4165
    4165/5 = 833
    5 does not divide 833, so 5^2 is in the list

    833/7 = 119
    119/7 = 17
    7 does not divide 17, so 7^2 is in the list

    17 is prime, so the final factorization is

    2^3 5^2 7^2 17

    As you can see, the method is quite simple, but very cumbersome for large numbers.

  • math -

    Igot it now. Thank you so much

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