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BECE Mathematics 2019 Paper

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Question : 29

Total: 40

Express 72 as a product of prime factors.

$2^3 \times 3^2$
$2^2 \times 3^3$
$2^2 \times 3^2$
$2 \times 3$

Solution:

Concept:

Prime factors are numbers greater than

1

that are divisible only by

1

and themselves.

Write

72

as a product of only these prime numbers.

Explanation:

Divide

72

by the smallest prime,

2

.

72 \div 2 = 36

36 \div 2 = 18

18 \div 2 = 9

Now

9

is not divisible by

2

, so divide by the next prime,

3

.

9 \div 3 = 3

3 \div 3 = 1

So the prime factors are

2, 2, 2, 3, 3

.

Group the same primes using exponents:

There are three

2

's and two

3

's.

Therefore,

72 = 2^3 \times 3^2

.

Answer:

72 = 2^3 \times 3^2

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