• A number that divides another number completely.
• The factors of \(12\) are \(1, 2,3,4,6\) and \(12\).

Is \(12\) the factor of \(36\)?

\(36\div 12=3\)

Thus, \(12\) is the factor of \(36\).

Factor that is a prime number.

The factors of \(18\) are \(1, 2,3,6,9\) and \(18\).

Between these factors, \(2\) and \(3\) are prime numbers.

Thus, the prime factors of \(18\) are \(2\) and \(3\).

Perform division repeatedly by dividing with the smallest prime number.

Division is continued until the quotient is \(1\).

\(\begin{array}{c} 2\\2\\3\\5 \\\phantom{-} \end{array} \begin{array}{|c} \quad60\quad\\ \hline \quad30\quad\\ \hline \quad15\quad\\ \hline \quad5\quad\\ \hline \quad1\quad\\ \end{array} \begin{array}{c}\end{array}\\\\\)

Thus, 

\(60=2\times2\times3\times5\).

Thus, 

\(60=2\times2\times3\times5\).

A number that is a factor of a few other numbers.

Determine whether \(6\) is a common factor of \(24\) and \(36\).

\(24\div6=4 \\36\div6=6\)

\(24\) and \(36\) can be divided completely by \(6\).

Thus, \(6\) is a common factor of \(24\) and \(36\).

The greatest number among the common factors.

(i) Determine the highest common factor of \(18\) and \( 24\).

Listing the common factors:

Factors of \(18 : 1 , 2 , 3 , 6 , 9, 18\)

Factors of \(24 : 1 , 2 , 3 , 4 , 6 , 8, 12, 24\)

So, the common factors of \(18 \) and \(24\) is \(1, 2, 3 \) and \(6\).

Thus, HCF is \(6\).

(ii) Determine the highest common factor of \(30,60\) and \( 72\).

Repeated division:

\(\begin{array}{c} 2\\2\\3 \\\phantom{-} \end{array} \begin{array}{|c} \quad36,\,60,\,72\quad\\ \hline \quad18,\,30,\,36\quad\\ \hline \quad9,\,15,\,18\quad\\ \hline \quad3,\,5,\,6\quad\\ \end{array} \begin{array}{c}\end{array}\\\\\)

Thus, HCF of \(36, 60\) and \(72\) is

\(2\times2\times3 = 12\).

(iii) Determine the highest common factor of \(48,64\) and \(80\).

Prime factorisation:

\(48 = 2\times2\times 2\times2\times3\)

\(64 = 2 × 2 × 2 × 2 × 2 × 2 \)

\(80 = 2\times2\times 2\times 2\times5\)

Thus, HCF is

\(2 × 2 × 2 × 2 = 16\).

• A number that divides another number completely.
• The factors of \(12\) are \(1, 2,3,4,6\) and \(12\).

Is \(12\) the factor of \(36\)?

\(36\div 12=3\)

Thus, \(12\) is the factor of \(36\).

Factor that is a prime number.

The factors of \(18\) are \(1, 2,3,6,9\) and \(18\).

Between these factors, \(2\) and \(3\) are prime numbers.

Thus, the prime factors of \(18\) are \(2\) and \(3\).

Perform division repeatedly by dividing with the smallest prime number.

Division is continued until the quotient is \(1\).

\(\begin{array}{c} 2\\2\\3\\5 \\\phantom{-} \end{array} \begin{array}{|c} \quad60\quad\\ \hline \quad30\quad\\ \hline \quad15\quad\\ \hline \quad5\quad\\ \hline \quad1\quad\\ \end{array} \begin{array}{c}\end{array}\\\\\)

Thus, 

\(60=2\times2\times3\times5\).

Thus, 

\(60=2\times2\times3\times5\).

A number that is a factor of a few other numbers.

Determine whether \(6\) is a common factor of \(24\) and \(36\).

\(24\div6=4 \\36\div6=6\)

\(24\) and \(36\) can be divided completely by \(6\).

Thus, \(6\) is a common factor of \(24\) and \(36\).

The greatest number among the common factors.

(i) Determine the highest common factor of \(18\) and \( 24\).

Listing the common factors:

Factors of \(18 : 1 , 2 , 3 , 6 , 9, 18\)

Factors of \(24 : 1 , 2 , 3 , 4 , 6 , 8, 12, 24\)

So, the common factors of \(18 \) and \(24\) is \(1, 2, 3 \) and \(6\).

Thus, HCF is \(6\).

(ii) Determine the highest common factor of \(30,60\) and \( 72\).

Repeated division:

\(\begin{array}{c} 2\\2\\3 \\\phantom{-} \end{array} \begin{array}{|c} \quad36,\,60,\,72\quad\\ \hline \quad18,\,30,\,36\quad\\ \hline \quad9,\,15,\,18\quad\\ \hline \quad3,\,5,\,6\quad\\ \end{array} \begin{array}{c}\end{array}\\\\\)

Thus, HCF of \(36, 60\) and \(72\) is

\(2\times2\times3 = 12\).

(iii) Determine the highest common factor of \(48,64\) and \(80\).

Prime factorisation:

\(48 = 2\times2\times 2\times2\times3\)

\(64 = 2 × 2 × 2 × 2 × 2 × 2 \)

\(80 = 2\times2\times 2\times 2\times5\)

Thus, HCF is

\(2 × 2 × 2 × 2 = 16\).