Will a number divisible by 6 necessarily be divisible by 2?
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Will a number divisible by 6 necessarily be divisible by 2?
In order to determine if a number divisible by 6 is also divisible by 2, we first review the divisibility rules:
Consider a number that is divisible by 6. By definition, since 6 itself factors into 2 multiplied by 3, any number divisible by 6 must be divisible by 2 and 3. This means that any number divisible by 6 is automatically divisible by 2 because 2 is a part of its factorization.
Therefore, yes, any number divisible by 6 will necessarily be divisible by 2 as per the rule of divisibility.
Thus, the correct choice is:
This conclusion adheres strictly to divisibility rules and confirms the assertion that being divisible by 6 includes being divisible by 2.
Yes
Determine if the following number is divisible by 3:
\( 352 \)
Because 6 = 2 × 3! When a number is divisible by 6, it means 6 goes into it evenly. Since 6 contains the factor 2, that factor 2 must also divide the number.
Sure! Take 18: it's divisible by 6 because 18 ÷ 6 = 3. Since 18 = 6 × 3 = (2 × 3) × 3 = 2 × 9, we see that 2 divides 18 as well (18 ÷ 2 = 9).
Same principle! If a number is divisible by 4, it must be divisible by 2 (since 4 = 2 × 2). If divisible by 8, it's divisible by both 4 and 2. Composite numbers always pass on their prime factors.
Yes! This is a fundamental property: if number a divides number b, and c divides a, then c must also divide b. It's called the transitivity of divisibility.
Think of it like ingredients in a recipe: if you need 6 cups of something, you're really using 2 groups of 3 cups each. The '2' is always there as part of the '6'!
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