Answer :
To determine if [tex]$8$[/tex] is a factor of a number, we check if dividing that number by [tex]$8$[/tex] results in a remainder of [tex]$0$[/tex]. In other words, if for a given number [tex]$n$[/tex], we have
[tex]$$
n \div 8 = \text{an integer with remainder } 0,
$$[/tex]
then [tex]$8$[/tex] is a factor of [tex]$n$[/tex].
Let's consider each number one by one:
1. For [tex]$80$[/tex]:
We compute
[tex]$$
80 \div 8 = 10 \quad \text{with a remainder } 0.
$$[/tex]
Since the remainder is [tex]$0$[/tex], [tex]$8$[/tex] is a factor of [tex]$80$[/tex].
2. For [tex]$24$[/tex]:
We compute
[tex]$$
24 \div 8 = 3 \quad \text{with a remainder } 0.
$$[/tex]
The remainder is [tex]$0$[/tex], so [tex]$8$[/tex] is a factor of [tex]$24$[/tex].
3. For [tex]$70$[/tex]:
We compute
[tex]$$
70 \div 8 = 8 \quad \text{with a remainder } 70 - 8 \times 8 = 70 - 64 = 6.
$$[/tex]
Since the remainder is [tex]$6$[/tex], [tex]$8$[/tex] is not a factor of [tex]$70$[/tex].
4. For [tex]$63$[/tex]:
We compute
[tex]$$
63 \div 8 = 7 \quad \text{with a remainder } 63 - 8 \times 7 = 63 - 56 = 7.
$$[/tex]
The remainder is [tex]$7$[/tex], so [tex]$8$[/tex] is not a factor of [tex]$63$[/tex].
5. For [tex]$8$[/tex]:
We compute
[tex]$$
8 \div 8 = 1 \quad \text{with a remainder } 0.
$$[/tex]
The remainder is [tex]$0$[/tex], meaning [tex]$8$[/tex] is indeed a factor of itself.
6. For [tex]$46$[/tex]:
We compute
[tex]$$
46 \div 8 = 5 \quad \text{with a remainder } 46 - 8 \times 5 = 46 - 40 = 6.
$$[/tex]
The remainder is [tex]$6$[/tex], so [tex]$8$[/tex] is not a factor of [tex]$46$[/tex].
Based on these calculations, the numbers for which [tex]$8$[/tex] is a factor are:
[tex]$$
80,\quad 24,\quad 8.
$$[/tex]
Thus, the correct answers are:
A. [tex]$80$[/tex], B. [tex]$24$[/tex], and E. [tex]$8$[/tex].
[tex]$$
n \div 8 = \text{an integer with remainder } 0,
$$[/tex]
then [tex]$8$[/tex] is a factor of [tex]$n$[/tex].
Let's consider each number one by one:
1. For [tex]$80$[/tex]:
We compute
[tex]$$
80 \div 8 = 10 \quad \text{with a remainder } 0.
$$[/tex]
Since the remainder is [tex]$0$[/tex], [tex]$8$[/tex] is a factor of [tex]$80$[/tex].
2. For [tex]$24$[/tex]:
We compute
[tex]$$
24 \div 8 = 3 \quad \text{with a remainder } 0.
$$[/tex]
The remainder is [tex]$0$[/tex], so [tex]$8$[/tex] is a factor of [tex]$24$[/tex].
3. For [tex]$70$[/tex]:
We compute
[tex]$$
70 \div 8 = 8 \quad \text{with a remainder } 70 - 8 \times 8 = 70 - 64 = 6.
$$[/tex]
Since the remainder is [tex]$6$[/tex], [tex]$8$[/tex] is not a factor of [tex]$70$[/tex].
4. For [tex]$63$[/tex]:
We compute
[tex]$$
63 \div 8 = 7 \quad \text{with a remainder } 63 - 8 \times 7 = 63 - 56 = 7.
$$[/tex]
The remainder is [tex]$7$[/tex], so [tex]$8$[/tex] is not a factor of [tex]$63$[/tex].
5. For [tex]$8$[/tex]:
We compute
[tex]$$
8 \div 8 = 1 \quad \text{with a remainder } 0.
$$[/tex]
The remainder is [tex]$0$[/tex], meaning [tex]$8$[/tex] is indeed a factor of itself.
6. For [tex]$46$[/tex]:
We compute
[tex]$$
46 \div 8 = 5 \quad \text{with a remainder } 46 - 8 \times 5 = 46 - 40 = 6.
$$[/tex]
The remainder is [tex]$6$[/tex], so [tex]$8$[/tex] is not a factor of [tex]$46$[/tex].
Based on these calculations, the numbers for which [tex]$8$[/tex] is a factor are:
[tex]$$
80,\quad 24,\quad 8.
$$[/tex]
Thus, the correct answers are:
A. [tex]$80$[/tex], B. [tex]$24$[/tex], and E. [tex]$8$[/tex].
