Find the HCF of 3³ × 5² and 3² × 5^4.

Correct Answer is : 32×523² × 5²32×52

Correct Answer is : 32×523² × 5²32×52

Test Index

BECE Mathematics 2011 Paper

Question : 13

Total: 40

3^3 \times 5^2

3^2 \times 5^4

Solution:

Concept:

The HCF is the product of the common prime factors, each raised to its smallest power.

Explanation:

The numbers are

3^3 \times 5^2

and

3^2 \times 5^4

For prime

3

, the powers are

3

and

2

The lowest power is

2

, so take

3^2

For prime

5

, the powers are

2

and

4

The lowest power is

2

, so take

5^2

Multiply the common prime factors with their lowest powers:

\mathrm{HCF} = 3^2 \times 5^2

Answer:

3^2 \times 5^2

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