John is thinking of a number. He gives the following 3 clues. “My number has 125 as a factor. My number is a multiple of 30. My number is b

Question

John is thinking of a number. He gives the following 3 clues. “My number has 125 as a factor. My number is a multiple of 30. My number is between 800 and 2000.” What is John’s number?

Please answer correctly

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Serenity 2 weeks 2021-09-12T08:37:51+00:00 1 Answer 0

Answers ( )

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    2021-09-12T08:39:35+00:00

    Answer:

    John’s number is 1500

    Step-by-step explanation:

    * Lets explain how to solve the problem

    – Factors of a number are the numbers you multiply to get the number

    – Ex: Factors of 12 are 1 × 12 , 2 × 6 , 3 × 4

    – The factors of a number smaller than or equal the number

    – Multiple of a number is that number multiplied by an integer

    – Ex: 2, 4, 6, 8, and 10 are multiples of 2

    – The multiples of a number greater than or equal the number

    * Lets solve the number

    – John is thinking of a number

    – He gives the following 3 clues

    # The number has 125 as a factor

    # The number is a multiple of 30

    # The number is between 800 and 2000

    ∵ 125 is a factor of the number

    – Assume that the number is 125 (its factors 1 , 5 , 25 , 125)

    ∵ The number is a multiple of 30

    – Assume the number is 30 (the first multiple of 30)

    – To solve the problem lets find the lowest common multiple of 125

      and 30 by using prime numbers only

    ∵ The prime factors of 125 = 5 × 5 × 5

    ∵ The prime factors of 30 = 2 × 3 × 5

    – L.C.M of the two numbers is the product of their prime factors

     without reputation

    ∴ L.C.M = 5 × 5 × 5 × 2 × 3 = 750

    ∵ 750 has 125 as a factor

    ∵ 750 is a multiple of 30

    – But 750 is not between 800 and 2000

    ∴ Find a multiple of 750 and between 800 and 2000

    ∵ 2 × 750 = 1500

    * lets check the three clues

    ∵ 1500 has 125 as a factor

    ∵ 1500 is a multiple of 30

    ∵ 1500 is between 800 and 2000

    ∴ John’s number is 1500

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