Deconstructing 32: Prime Factors and Mathematical Insights

Q: Why isn't 32 divisible by 10 if it's even?

Being divisible by 10 requires ending in 0, not just being even. Since 32 ends in 2, it's divisible by 2 but not by 10!

Q: How do I remember the divisibility rule for 4?

Look at the last two digits only! If those digits form a number divisible by 4, then the whole number is divisible by 4. For 32: the last two digits are 32, and $ 32 \div 4 = 8 $.

Q: Can a number be divisible by 2 but not by 4?

Yes! Numbers like 6, 10, 14, 18 are divisible by 2 but not by 4. Being divisible by 2 means it's even, but divisibility by 4 has a stricter rule.

Q: What's the difference between 'divisible by 2' and 'divisible by 2 and 4'?

The first option is incomplete - it only mentions one factor. The correct answer includes both factors that 32 is actually divisible by, making it the most complete choice.

Q: Do I need to do actual division to check divisibility?

No! Use the divisibility rules as shortcuts: For 2: last digit evenFor 4: last two digits divisible by 4For 10: last digit is 0

Divisibility Rules with Multiple Factor Analysis

The number 32...

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Step-by-step written solution

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Understand the problem

The number 32...

Step-by-step solution

To determine the divisibility of 32, we'll use divisibility rules:

Step 1: Divisibility by 2
A number is divisible by 2 if its last digit is even. The last digit of 32 is 2, which is even. Therefore, 32 is divisible by 2.
Step 2: Divisibility by 4
A number is divisible by 4 if the number formed by its last two digits is divisible by 4. Here, the number formed by the last two digits is 32. Since $32 \div 4 = 8$ , which is an integer, 32 is divisible by 4.
Step 3: Divisibility by 10
A number is divisible by 10 if its last digit is 0. The last digit of 32 is 2, not 0. Therefore, 32 is not divisible by 10.

Considering the choices provided, the correct statement is that 32 is divisible by both 2 and 4 but not by 10.

Therefore, the solution to the problem is ...is divisible by 2 and also by 4.

Final Answer

...is divisible by 2 and also by 4.

Key Points to Remember

Essential concepts to master this topic

Rule: Check last digit for divisibility by 2 and 10
Technique: For 4, check last two digits: $32 \div 4 = 8$
Check: Verify each divisor separately: 32÷2=16, 32÷4=8, both whole numbers ✓

Common Mistakes

Avoid these frequent errors

Testing only one divisibility rule instead of all options
Don't stop after finding 32 is divisible by 2 and assume other rules don't matter = missing the complete answer! This leads to choosing incomplete options. Always test every divisibility rule mentioned in the answer choices.

Practice Quiz

Test your knowledge with interactive questions

Is the number 43 divisible by 4?

FAQ

Everything you need to know about this question

Why isn't 32 divisible by 10 if it's even?

Being divisible by 10 requires ending in 0, not just being even. Since 32 ends in 2, it's divisible by 2 but not by 10!

How do I remember the divisibility rule for 4?

Look at the last two digits only! If those digits form a number divisible by 4, then the whole number is divisible by 4. For 32: the last two digits are 32, and $32 \div 4 = 8$ .

Can a number be divisible by 2 but not by 4?

Yes! Numbers like 6, 10, 14, 18 are divisible by 2 but not by 4. Being divisible by 2 means it's even, but divisibility by 4 has a stricter rule.

What's the difference between 'divisible by 2' and 'divisible by 2 and 4'?

The first option is incomplete - it only mentions one factor. The correct answer includes both factors that 32 is actually divisible by, making it the most complete choice.

Do I need to do actual division to check divisibility?

No! Use the divisibility rules as shortcuts:

For 2: last digit even
For 4: last two digits divisible by 4
For 10: last digit is 0

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