# Is 143 prime or composite?

degeneratecircle | High School Teacher | (Level 2) Associate Educator

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Every integer is either prime or can be factored into prime factors. One way to check if a number `n` is prime is to see if it's divisible by any of the primes up to `sqrt(n)`. Here, since `n=143` and `12<sqrt(143)<13`, we only have to check if 143 is divisible by primes up to 12.

Is 143 divisible by 2? No, since 143 is odd, it can't be divisible by 2.

Is 143 divisible by 3? No. One way to see this is to add 1+4+3, which equals 8. 8 isn't divisible by 3, so neither is 143. (See the link for more information on this method.) Another way is to recognize that 150 is divisible by 3, and 143 is 7 less than 150, but 7 isn't divisible by 3.

Is 143 divisible by 5? It doesn't end in 0 or 5, so no.

Is 143 divisible by 7? There is a rule for divisibility by 7 which I forget, but the easiest way to see that 143 isn't divisible by 7 is to recognize that 140 is divisible by 7, so 143 can't be.

Is 143 divisible by 11? Yes, which can be done mentally or by long division. It turns out that `143=11*13.`

143 is composite and can be factored as `143=11*13.`

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