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A farmer harvested 48 mangoes and 60 oranges. He packed them into identical baskets such that each basket had the same number of mangoes and same number of oranges, with no fruit left over. Determine: a) The highest number of baskets obtained. b) The number of mangoes in each basket

Mathematics

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Answers

2 parts
a

12 baskets\text{12 baskets}

b

4 mangoes\text{4 mangoes}

Step-by-step solution

4 steps

Part a· 3 steps

The highest number of baskets obtained.

  1. Find the prime factorization of 48 (number of mangoes).

    48=2×24=2×2×12=2×2×2×6=2×2×2×2×3=24×3148 = 2 \times 24 = 2 \times 2 \times 12 = 2 \times 2 \times 2 \times 6 = 2 \times 2 \times 2 \times 2 \times 3 = 2^4 \times 3^1

  2. Find the prime factorization of 60 (number of oranges).

    60=2×30=2×2×15=2×2×3×5=22×31×5160 = 2 \times 30 = 2 \times 2 \times 15 = 2 \times 2 \times 3 \times 5 = 2^2 \times 3^1 \times 5^1

  3. Determine the Highest Common Factor (HCF) by taking the lowest power of common prime factors.

    The common prime factors are 2 and 3.
    The lowest power of 2 is 222^2.
    The lowest power of 3 is 313^1.

    HCF(48,60)=22×31=4×3=12\text{HCF}(48, 60) = 2^2 \times 3^1 = 4 \times 3 = 12

    The highest number of baskets is 12.

    12 baskets\boxed{\text{12 baskets}}

Part b

4 mangoes\text{4 mangoes}

The number of mangoes in each basket.

  1. Divide the total number of mangoes by the highest number of baskets.

    Mangoes per basket=Total mangoesNumber of baskets=4812=4\text{Mangoes per basket} = \frac{\text{Total mangoes}}{\text{Number of baskets}} = \frac{48}{12} = 4

    The number of mangoes in each basket is 4.

    4 mangoes\boxed{\text{4 mangoes}}
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