Let's solve the exercise step by step:
Part 1: Fill in the blanks
a. 2, 3, 5 are prime factors of 30.
The prime factors of 30 are 2, 3, and 5 because 30 = 2 × 3 × 5.
b. The prime factors of 41 are 1 and 41.
41 is a prime number, and its only prime factors are 1 and 41.
c. There are 2 prime factors of 58.
The prime factors of 58 are 2 and 29 (58 = 2 × 29).
d. The prime factors of 10 are 2 and 5.
10 = 2 × 5, so its prime factors are 2 and 5.
e. Prime factors can never be a composite number.
Prime factors are always prime numbers, not composite.
Part 2: State whether the following are true or false
a. The prime factor of a number divides the number completely.
True: By definition, a prime factor divides the number exactly with no remainder.
b. The prime factors of 100 are 2, 3, 5, 5, 10.
False: The correct prime factors of 100 are 2 and 5 (100 = 2 × 2 × 5 × 5).
c. A factor tree is used to find prime factors.
True: A factor tree is a method of breaking down a number into its prime factors.
d. Prime factors of numbers are prime numbers.
True: By definition, prime factors are prime numbers.
e. 2 is the only prime factor of the number 6.
False: The prime factors of 6 are 2 and 3 (6 = 2 × 3).
Summary of answers:
1. Fill in the blanks:
o a. 2, 3, 5
o b. 1 and 41
o c. 2
o d. 2 and 5
o e. composite
2. True or False:
o a. True
o b. False
o c. True
o d. True
o e. False
Let me know if you need any further explanations! Let's go through each question step by step:
Part 3: Select the correct answer from the given options
a. 3, 3, 3, and 5 are prime factors of:
The prime factors are 3, 3, 3, and 5. So, the number they form is 3 × 3
× 3 × 5 = 135.
o Correct answer: D (135)
b. The prime factors of 110 are:
The prime factors of 110 are 2, 5, and 11 (110 = 2 × 5 × 11).
o Correct answer: B (2, 5, 11)
c. The prime factors of 50 are 2, 5 and:
The prime factors of 50 are 2 and 5 (50 = 2 × 5 × 5).
o Correct answer: C (5)
d. The prime factor is always:
The prime factor of any number is always a prime number, because it
divides the number without a remainder.
o Correct answer: A (a prime number)
Summary of answers:
a. D (135)
b. B (2, 5, 11)
c. C (5)
d. A (a prime number)
Let me know if you need any further explanations! Let's break down and solve the exercise:
Part 1: Prime factorisation means
Prime factorisation refers to breaking a number into prime factors.
Correct answer: D (breaking a number into prime factors)
Part 4: Draw factor trees to show the prime factors of the given numbers.
We'll break down each number into its prime factors. Here's how we do it:
a. 15:
15 = 3 × 5 (both 3 and 5 are prime numbers).
b. 20:
20 = 2 × 10, and 10 = 2 × 5.
So, 20 = 2 × 2 × 5 (prime factors are 2 and 5).
c. 14:
14 = 2 × 7 (both 2 and 7 are prime numbers).
d. 8:
8 = 2 × 4, and 4 = 2 × 2.
So, 8 = 2 × 2 × 2 (prime factor is 2).
e. 21:
21 = 3 × 7 (both 3 and 7 are prime numbers).
f. 22:
22 = 2 × 11 (both 2 and 11 are prime numbers).
g. 16:
16 = 2 × 8, and 8 = 2 × 4, and 4 = 2 × 2.
So, 16 = 2 × 2 × 2 × 2 (prime factor is 2).
h. 27:
27 = 3 × 9, and 9 = 3 × 3.
So, 27 = 3 × 3 × 3 (prime factor is 3).
Part 5: Draw as many different factor trees as you can to show the prime factors of
these numbers.
a. 40:
40 = 2 × 20, and 20 = 2 × 10, and 10 = 2 × 5.
So, 40 = 2 × 2 × 2 × 5 (prime factors are 2 and 5).
b. 48:
48 = 2 × 24, and 24 = 2 × 12, and 12 = 2 × 6, and 6 = 2 × 3.
So, 48 = 2 × 2 × 2 × 2 × 3 (prime factors are 2 and 3).
c. 60:
60 = 2 × 30, and 30 = 2 × 15, and 15 = 3 × 5.
So, 60 = 2 × 2 × 3 × 5 (prime factors are 2, 3, and 5).
d. 24:
24 = 2 × 12, and 12 = 2 × 6, and 6 = 2 × 3.
So, 24 = 2 × 2 × 2 × 3 (prime factors are 2 and 3).
e. 50:
50 = 2 × 25, and 25 = 5 × 5.
So, 50 = 2 × 5 × 5 (prime factors are 2 and 5).
f. 72:
72 = 2 × 36, and 36 = 2 × 18, and 18 = 2 × 9, and 9 = 3 × 3.
So, 72 = 2 × 2 × 2 × 3 × 3 (prime factors are 2 and 3).
Part 6: Find the prime factors of these numbers using the division method.
a. 84:
84 ÷ 2 = 42, 42 ÷ 2 = 21, 21 ÷ 3 = 7.
So, 84 = 2 × 2 × 3 × 7 (prime factors are 2, 3, and 7).
b. 117:
117 ÷ 3 = 39, 39 ÷ 3 = 13.
So, 117 = 3 × 3 × 13 (prime factors are 3 and 13).
c. 333:
333 ÷ 3 = 111, 111 ÷ 3 = 37.
So, 333 = 3 × 3 × 37 (prime factors are 3 and 37).
d. 126:
126 ÷ 2 = 63, 63 ÷ 3 = 21, 21 ÷ 3 = 7.
So, 126 = 2 × 3 × 3 × 7 (prime factors are 2, 3, and 7).
e. 520:
520 ÷ 2 = 260, 260 ÷ 2 = 130, 130 ÷ 2 = 65, 65 ÷ 5 = 13.
So, 520 = 2 × 2 × 2 × 5 × 13 (prime factors are 2, 5, and 13).
f. 99:
99 ÷ 3 = 33, 33 ÷ 3 = 11.
So, 99 = 3 × 3 × 11 (prime factors are 3 and 11).
Summary:
Prime factorisation means: D (breaking a number into prime
factors)
Prime factor trees for the numbers:
o 15 → 3 × 5
o 20 → 2 × 2 × 5
o 14 → 2 × 7
o 8→2×2×2
o 21 → 3 × 7
o 22 → 2 × 11
o 16 → 2 × 2 × 2 × 2
o 27 → 3 × 3 × 3
Factor trees for the numbers:
o 40 → 2 × 2 × 2 × 5
o 48 → 2 × 2 × 2 × 2 × 3
o 60 → 2 × 2 × 3 × 5
o 24 → 2 × 2 × 2 × 3
o 50 → 2 × 5 × 5
o 72 → 2 × 2 × 2 × 3 × 3
Prime factors using division method:
o 84 → 2 × 2 × 3 × 7
o 117 → 3 × 3 × 13
o 333 → 3 × 3 × 37
o 126 → 2 × 3 × 3 × 7
o 520 → 2 × 2 × 2 × 5 × 13
o 99 → 3 × 3 × 11
Let me know if you'd like any further details!
