Thursday, 13 March 2014

3rd Question

FACTORS 1:
Determine whether or not each number is a common factor of 144 and 240. Try to use different methods, and SHOW YOUR WORK.

a) 2   b) 3   c) 10   d) 48   e) 120

9 comments:

  1. a) 2 is an even number and so is 144 and 240. 2 goes in evenly to both numbers,it is a common factor.

    b) 144/3 = 48 240/3= 80 2 is a common factor.

    c) even though 10 can go in to 240 without a remainder the same can not be said with 144 which would have 4 as a remainder. 10 is not a common factor

    d) 144/40=3.6 without even looking at 240 we know 40 cannot be a factor of both numbers. 40 isnt a common factor.

    e) when you double 120 you get 240 but 120 is too close in value to 144 to fit in another time, meaning it can only go in to one of the two numbers. 120 is not a common factor.

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  2. a) 2 is a common factor because it is an even number and so are 144 and 240.
    b) 3 x 12 = 36. 36 x 4 = 144. 36 does not go into 240. 36 is not a common number.
    c) 10 x 12 = 120. 120 x 2 = 240. 10 does not go into 144. 10 is not a common factor.
    d) 48 x 3 = 144. 48 x 5 = 240. 48 goes into both 144 and 240. 48 is a common factor.
    e) 120 x 2 = 240. So that means there is no possible way 120 could go into 144. Also considering that 120 and 144 are just 24 numbers apart.

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  3. a) 2 is defanetly a common factor of these numbers because they are both even and 2 skips every odd number
    b) 144 and 240 are multiples of because 1+4+4=9 and 2+4+0=6, 9 and 6 are multiples of 3
    c) 144 is not a multiple of 10 because the last diget of 144 is not 0 but 240 is a multiple because the last diget is 0
    d) 144/48 is 3 and 240/48 is 5, therefor 48 is a factor of both 144 and 240
    e) 144 is not a multiple of 120, though it is grater than 144, the first multiple is 120, therefor it skip counts by 120

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  8. 3a)

    144
    / \
    72 2
    / \
    36 2
    / \
    18 2
    / \
    9 2
    / \
    3 3

    b)

    240
    / \
    120 2
    / \
    60 2
    / \
    30 2
    / \
    15 2
    / \
    5 3

    The factoring trees show that 2 and 3 are both common factors.

    c) 10 is not a common factor of 144 and 240 because there is no "0" at the end of 144. It goes into 240 24 times.

    d) 48 is a common factor. 144 / 48 = 3 240 / 48 = 5

    e) 120 is not a common factor of 144 and 240. Common factors will end in 0 and a 144 ends in a 0. 120 is a factor of 240. 240 / 2 = 120.

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  9. e) My correction is common factors will end in 0 and 144 ends in a 4.

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