Question
Show that 101 is prime by showing that 101 has no prime divisors $d$ such that $1<d^2 \leq 101$.
Step 1
The square root of 101 is approximately 10.05, so we need to consider prime numbers less than or equal to 10. Show more…
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What can we do to show that 101 is prime? We can determine whether the greatest prime smaller than 101 (7 in this case) is a factor of 101. If 7 divides 101, then 101 is not a prime number. We can divide 101 by all uneven numbers smaller than 101 and greater than 2. If 101 is not divisible by any of these numbers, then 101 is prime. We can determine whether any number smaller than 101 and greater than 1 divides 101. If there is such a number, then 101 is not prime. We can determine whether any prime smaller than 101 is a factor of 101. If none of {2, 3, 5, 7} divides 101, then 101 is prime.
Write the prime factorization of the number if it is not a prime number. If a number is prime, write prime. $$ 101 $$
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