Part C-Extended-response question ( 6 marks) A florist wholesaler has a delivery of 1176 roses, 1260 tulips and 1350 gerberas from flower arowers. Write each number in prime factor form. Draw factor trees or use repeated divisions to find the factors.

To express each of these numbers in prime factor form, we can use the method of repeated division by prime numbers. Starting with 1176: 1176 ÷ 2 = 588 588 ÷ 2 = 294 294 ÷ 2 = 147 147 ÷ 3 = 49 49 ÷ 7 = 7 7 ÷ 7 = 1 So, the prime factorization of 1176 is \( 2^3 \times 3^1 \times 7^2 \). Next, for 1260: 1260 ÷ 2 = 630 630 ÷ 2 = 315 315 ÷ 3 = 105 105 ÷ 3 = 35 35 ÷ 5 = 7 7 ÷ 7 = 1 Thus, the prime factorization of 1260 is \( 2^2 \times 3^2 \times 5^1 \times 7^1 \). Finally, for 1350: 1350 ÷ 2 = 675 675 ÷ 3 = 225 225 ÷ 3 = 75 75 ÷ 3 = 25 25 ÷ 5 = 5 5 ÷ 5 = 1 Therefore, the prime factorization of 1350 is \( 2^1 \times 3^3 \times 5^2 \). In summary: - 1176 = \( 2^3 \times 3^1 \times 7^2 \) - 1260 = \( 2^2 \times 3^2 \times 5^1 \times 7^1 \) - 1350 = \( 2^1 \times 3^3 \times 5^2 \)