Question

10 which statements are true? choose all the correct answers.
a 25 is a factor of 5.
b 25 is a multiple of 5.
c 5 is a multiple of 40.
d 5 is a factor of 40.
e for every factor of 5, 5 is a multiple of that number.
f for every multiple of 5, 5 is a factor of that number.

Explanation:

Step1: Recall factor and multiple definitions

A factor of a number \( n \) is an integer that divides \( n \) without leaving a remainder. A multiple of a number \( n \) is an integer obtained by multiplying \( n \) by another integer.

Step2: Analyze statement A

Check if 25 divides 5. \( 5\div25 = 0.2 \), not an integer. So 25 is not a factor of 5.

Step3: Analyze statement B

Check if 25 is a multiple of 5. \( 25\div5 = 5 \), an integer. So 25 is a multiple of 5.

Step4: Analyze statement C

Check if 5 is a multiple of 40. \( 5\div40 = 0.125 \), not an integer. So 5 is not a multiple of 40.

Step5: Analyze statement D

Check if 5 is a factor of 40. \( 40\div5 = 8 \), an integer. So 5 is a factor of 40.

Step6: Analyze statement E

Let \( f \) be a factor of 5. Then \( 5\div f \) is an integer, so \( 5 = f\times k \) (where \( k \) is an integer), meaning 5 is a multiple of \( f \). So this statement is true.

Step7: Analyze statement F

Let \( m \) be a multiple of 5. Then \( m = 5\times k \) (where \( k \) is an integer), so \( m\div5 = k \), an integer. Thus, 5 is a factor of \( m \). So this statement is true.

Answer:

B. 25 is a multiple of 5,
D. 5 is a factor of 40,
E. For every factor of 5, 5 is a multiple of that number,
F. For every multiple of 5, 5 is a factor of that number