A number divisible by 10 is always divisible by 2 and 5.
Understanding Divisibility by 10
The number 10 is a composite number, meaning it has factors other than 1 and itself. Its prime factorization is 2 x 5. This means any number that is a multiple of 10 must also contain both 2 and 5 as factors. Therefore, it will be divisible by both 2 and 5.
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Example: Consider the number 120. It's divisible by 10 (120 / 10 = 12). It's also divisible by 2 (120 / 2 = 60) and 5 (120 / 5 = 24).
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Proof: Let n be a number divisible by 10. This means that n = 10k for some integer k. Since 10 = 2 x 5, we can rewrite this as n = 2 x 5 x k. This clearly shows that n is divisible by both 2 and 5.
This concept is fundamental in number theory and is useful for various mathematical operations and problem-solving. Understanding the prime factorization of a number reveals important divisibility properties. Reference materials confirm this rule, stating that a number divisible by 10 is always divisible by 2 and 5. [A number is divisible by 10 is always divisible by 2 and 5......05-Jul-2020]
The provided references offer related information on divisibility rules for other numbers but do not contradict this fundamental rule.
