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Find the factors of the following numbers: a. 40 (k) 96 (c) 75 (d) 180 (e) 104

Mathematics

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Answers

5 parts
a
1, 2, 4, 5, 8, 10, 20, 40
b
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
c
1, 3, 5, 15, 25, 75
d
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
e
1, 2, 4, 8, 13, 26, 52, 104

Step-by-step solution

10 steps

Here are the factors for each number:

Part a· 2 steps

Factors of 40

  1. List pairs of numbers that multiply to 40.

    1×40=401 \times 40 = 40 2×20=402 \times 20 = 40 4×10=404 \times 10 = 40 5×8=405 \times 8 = 40
  2. Collect all unique factors in ascending order.

    The factors of 40 are 1,2,4,5,8,10,20,401, 2, 4, 5, 8, 10, 20, 40.

    1,2,4,5,8,10,20,40\boxed{1, 2, 4, 5, 8, 10, 20, 40}

Part b1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

Factors of 96

  1. List pairs of numbers that multiply to 96.

    1×96=961 \times 96 = 96 2×48=962 \times 48 = 96 3×32=963 \times 32 = 96 4×24=964 \times 24 = 96 6×16=966 \times 16 = 96 8×12=968 \times 12 = 96
  2. Collect all unique factors in ascending order.

    The factors of 96 are 1,2,3,4,6,8,12,16,24,32,48,961, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96.

    1,2,3,4,6,8,12,16,24,32,48,96\boxed{1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96}

Part c1, 3, 5, 15, 25, 75

Factors of 75

  1. List pairs of numbers that multiply to 75.

    1×75=751 \times 75 = 75 3×25=753 \times 25 = 75 5×15=755 \times 15 = 75
  2. Collect all unique factors in ascending order.

    The factors of 75 are 1,3,5,15,25,751, 3, 5, 15, 25, 75.

    1,3,5,15,25,75\boxed{1, 3, 5, 15, 25, 75}

Part d1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180

Factors of 180

  1. List pairs of numbers that multiply to 180.

    1×180=1801 \times 180 = 180 2×90=1802 \times 90 = 180 3×60=1803 \times 60 = 180 4×45=1804 \times 45 = 180 5×36=1805 \times 36 = 180 6×30=1806 \times 30 = 180 9×20=1809 \times 20 = 180 10×18=18010 \times 18 = 180 12×15=18012 \times 15 = 180
  2. Collect all unique factors in ascending order.

    The factors of 180 are 1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,1801, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180.

    1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,180\boxed{1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180}

Part e1, 2, 4, 8, 13, 26, 52, 104

Factors of 104

  1. List pairs of numbers that multiply to 104.

    1×104=1041 \times 104 = 104 2×52=1042 \times 52 = 104 4×26=1044 \times 26 = 104 8×13=1048 \times 13 = 104
  2. Collect all unique factors in ascending order.

    The factors of 104 are 1,2,4,8,13,26,52,1041, 2, 4, 8, 13, 26, 52, 104.

    1,2,4,8,13,26,52,104\boxed{1, 2, 4, 8, 13, 26, 52, 104}
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