Maths Olympiad Prep

Track / Stage 3 / 76 of 260 #76 of 1964

Problem 76

AMC 10/12, early questions
Number theory Difficulty 3.3 Find the answer

A composite number has at least 3 divisors. \_\_\_\_\_\_. (Judge true or false)

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

Solution: According to the definition of a composite number,
a composite number, besides 1 and itself, must have at least one other factor, meaning it has at least 3 factors.
Therefore, the statement that a composite number has at least 3 factors is correct.
Hence, the answer is: True\boxed{\text{True}}.
In natural numbers, a number that has factors other than 1 and itself is a composite number. From this, it is known that a composite number, besides 1 and itself, must have at least one other factor, meaning it has at least 3 factors, such as 9, which has three factors: 1, 9, and 3.
Understanding the definition of a composite number is key to solving this problem.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.