Sure, let's go through the solution step by step for each part of your questions.
### 5. Find the prime factors of the following numbers.
Prime factors are the prime numbers that divide a number exactly, without leaving a remainder.
a) 15
- Prime factors: 3, 5
- Explanation: 15 can be divided by 3 (15 ÷ 3 = 5) and 5 (5 ÷ 5 = 1).
b) 20
- Prime factors: 2, 2, 5
- Explanation: 20 can be divided by 2 repeatedly until it cannot be divided further (20 ÷ 2 = 10, 10 ÷ 2 = 5) and then by 5 (5 ÷ 5 = 1).
c) 27
- Prime factors: 3, 3, 3
- Explanation: 27 can be repeatedly divided by 3 (27 ÷ 3 = 9, 9 ÷ 3 = 3, 3 ÷ 3 = 1).
d) 30
- Prime factors: 2, 3, 5
- Explanation: 30 can be divided by 2 (30 ÷ 2 = 15), then by 3 (15 ÷ 3 = 5), and lastly by 5 (5 ÷ 5 = 1).
e) 36
- Prime factors: 2, 2, 3, 3
- Explanation: 36 can be divided by 2 repeatedly (36 ÷ 2 = 18, 18 ÷ 2 = 9) and then by 3 repeatedly (9 ÷ 3 = 3, 3 ÷ 3 = 1).
f) 42
- Prime factors: 2, 3, 7
- Explanation: 42 can be divided by 2 (42 ÷ 2 = 21), then by 3 (21 ÷ 3 = 7), and lastly by 7 (7 ÷ 7 = 1).
g) 48
- Prime factors: 2, 2, 2, 2, 3
- Explanation: 48 can be divided by 2 repeatedly (48 ÷ 2 = 24, 24 ÷ 2 = 12, 12 ÷ 2 = 6, 6 ÷ 2 = 3) and then by 3 (3 ÷ 3 = 1).
h) 63
- Prime factors: 3, 3, 7
- Explanation: 63 can be divided by 3 repeatedly (63 ÷ 3 = 21, 21 ÷ 3 = 7) and then by 7 (7 ÷ 7 = 1).
### 6. Find the first five multiples of the following numbers.
Multiples are the results of multiplying a number by integers.
a) 2
- Multiples: 2, 4, 6, 8, 10
b) 3
- Multiples: 3, 6, 9, 12, 15
c) 5
- Multiples: 5, 10, 15, 20, 25
d) 6
- Multiples: 6, 12, 18, 24, 30
e) 8
- Multiples: 8, 16, 24, 32, 40
f) 10
- Multiples: 10, 20, 30, 40, 50
g) 11
- Multiples: 11, 22, 33, 44, 55
h) 12
- Multiples: 12, 24, 36, 48, 60
i) 15
- Multiples: 15, 30, 45, 60, 75
j) 20
- Multiples: 20, 40, 60, 80, 100
k) 25
- Multiples: 25, 50, 75, 100, 125
l) 30
- Multiples: 30, 60, 90, 120, 150
### 7. Round off the following numbers to the nearest ten.
When rounding to the nearest ten, if the units digit is 5 or more, round up; if it's 4 or less, round down.
a) 642
- Rounded to: 640
b) 8745
- Rounded to: 8740
c) 49386
- Rounded to: 49390
d) 84
- Rounded to: 80
e) 9087
- Rounded to: 9090
f) 55555
- Rounded to: 55560
### 8. Round off the following numbers to the nearest hundred.
When rounding to the nearest hundred, if the tens digit is 5 or more, round up; if it's 4 or less, round down.
a) 347
- Rounded to: 300
b) 4892
- Rounded to: 4900
c) 7830
- Rounded to: 7800
d) 4894
- Rounded to: 4900
e) 66347
- Rounded to: 66300
f) 56675
- Rounded to: 56700
### 9. Round off the following numbers to the nearest thousand.
When rounding to the nearest thousand, if the hundreds digit is 5 or more, round up; if it's 4 or less, round down.
a) 6242
- Rounded to: 6000
b) 66732
- Rounded to: 67000
c) 48934
- Rounded to: 49000
d) 58327
- Rounded to: 58000
e) 67562
- Rounded to: 68000
f) 34082
- Rounded to: 34000
These results were derived using standard mathematical methods for finding prime factors, determining multiples, and rounding off numbers.
