Question

Find the values of x, y, z and w in the following factor tree. Also write the prime factorisation of x.

Answer 1

Given: A factor tree whose known leaves (bottom primes) are 2, 2, 3, 3, 13 and 7 and an internal node labelled 819.

Step-wise calculation:

1. w = 13 × 7 = 91.

2. z is the node above w with a factor 3, so z = 3 × w = 3 × 91 = 273.

Also 819 = 3 × z

⇒ z = 819 ÷ 3

⇒ z = 273

3. y is the node obtained by multiplying 2 and 819, so y = 2 × 819 = 1638.

4. x is the top node = 2 × y

= 2 × 1638

= 3276

Prime factorisation of x

x = 2 × y

= 2 × (2 × 819)

= 2² × 819

819 = 3 × 273

= 3 × (3 × 91)

= 3² × 91

= 3² × 13 × 7

Therefore x = 2² × 3² × 7 × 13.