Prime Check - Arithmetic Step by Step

Decide whether 17 is prime by testing prime divisors up to the square root of 17. If none divide 17 evenly, the number is prime.

primality-test A prime number has exactly two factors: 1 and itself. To check, try dividing by each prime up to the square root. For 17, test 2 and 3. If any trial succeeds (remainder 0), the number is composite. Stop as soon as one works.

Example

Test whether 17 has any prime factor up to its square root.

highlighted = computed this step

Step 1 — Set up

Set up the numbers to test.

\mathrm{prime\ check:}\ 17

Step 2 — Test 2

Test divisibility: 17 ÷ 2 = 8 remainder 1.

17 \div \hl{2} = 8 \ \mathrm{r}\ \hl{1}

Step 3 — Test 3

Test divisibility: 17 ÷ 3 = 5 remainder 2.

17 \div \hl{3} = 5 \ \mathrm{r}\ \hl{2}

Step 4 — Verdict

17 is prime because no prime up to sqrt(17) divides it.

\text{17 is prime because no prime up to sqrt(17) divides it}