What are the factors of 14?

14 has 4 divisors in total: 1, 2, 7, 14. Its prime factorisation is 2 × 7, and every one of those 4 divisors is built from those primes. The divisor count follows directly from the exponents: (1 + 1) × (1 + 1) = 4. They sum to 24.

What is the nearest prime to 14?

The prime immediately below 14 is 13, and the one immediately above is 17. Since 14 is composite it sits inside the run between them, 3 numbers wide.

What is Euler's totient of 14?

φ(14) = 6. The totient counts how many numbers below 14 share no common factor with it. Computing it from the factorisation 2 × 7 gives 14 × (1 − 1/2) × (1 − 1/7) = 6.

What is a Mersenne prime?

A prime of the form 2^p − 1 where p is itself prime. 3, 7, 31 and 127 are the first four. The exponent being prime is necessary but nowhere near sufficient — 2¹¹ − 1 is 2,047, which is 23 × 89. They matter because there is a fast test that works only for numbers of this shape, which is why every record-breaking largest known prime for decades has been a Mersenne prime.

How does the number of divisors work?

It comes from the exponents in the factorisation, not from the size of the number. Add one to each exponent and multiply: 12 is 2² × 3, so it has (2+1) × (1+1) = 6 divisors. This is why a small number packed with low prime powers can have more divisors than a much larger one — 48 has ten, while 47 has two.

Is there a formula that produces only primes?

Nothing useful. Euler noticed that n² + n + 41 gives a prime for every n from 0 to 39, which is remarkable, but it fails at n = 40 where the result is 41². No polynomial with integer coefficients can produce primes for every input — it is a theorem, not merely an absence of cleverness. Formulas that do exist are far too slow to compute.

How large can a gap between primes be?

As large as you like. Take any number n and consider the run from n! + 2 up to n! + n: every one of them is composite, because n! + k is divisible by k. That constructs a gap of any length you choose. Gaps do appear early too — there is nothing between 23 and 29, and nothing between 89 and 97.

Are there patterns in where primes fall?

Every prime above 3 sits one away from a multiple of 6, which rules out four of every six numbers immediately. Beyond that the sequence is famously irregular: gaps vary unpredictably, and the deepest questions about their distribution, including the Riemann Hypothesis, remain open after more than a century and a half.

Is 14 a Prime Number?

14 is the product of 2 and 7, and the smallest number whose two prime factors are the first and fourth primes. It sits in a run of three consecutive composites, 14, 15 and 16, which is the sort of gap that becomes routine higher up. It is not prime. 14 = 2 × 7, so it has 4 divisors rather than two, ...

YOUR NUMBER

NUMBER

WORTH TRYING

14 IS

NOT PRIME

SMALLEST FACTOR

14 = 2 × 7

Prime factorisation

2 × 7

Number of divisors

Sum of divisors

Totient φ(n)

Previous prime

Next prime

FACTOR BREAKDOWN

PRIME

POWER

CONTRIBUTES

STEPS

Trial-divide 14 by every prime up to √14 ≈ 3 — beyond that a factor would have a partner below it

The smallest prime divisor is 2, so 14 is composite

Full factorisation: 2 × 7

14 is NOT prime

SIEVE OF ERATOSTHENES

Two thousand years old and still the fastest way. Take the first uncrossed number, 2, and strike out every multiple of it. Move to the next survivor, 3, and repeat. Each pass can start at the square of its prime, because anything smaller was already struck by a smaller factor — which is why the passes get shorter and stop entirely once the prime exceeds √100. Whatever survives is prime. Your number 14 is outlined in gold.

HOW MANY PRIMES BELOW x — AND WHAT THE THEORY PREDICTS

4 vs 4

100

25 vs 22

1,000

168 vs 145

10,000

1,229 vs 1,086

100,000

9,592 vs 8,686

Actual count against x ÷ ln x. At x = 10 the estimate overshoots slightly; from 100 upward it runs low, and from 1,000 onward the gap narrows steadily — a ratio of 1.16 at a thousand down to 1.10 at a hundred thousand. That it tends to 1 at all is the Prime Number Theorem, and how slowly it does so is why the proof took a century to find.

Proved, not guessed. Primality here uses a deterministic Miller–Rabin test with a fixed witness set that is proven correct for every number this page accepts, so a result of PRIME is a proof rather than a probability. Ranges are sieved up to 200,000; single numbers are tested up to 4,503,599,627,370,495.

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HOW TO USE

1
The answer is already on screen: 14 is not prime, because 14 = 2 × 7. Nothing needs typing — this page opens the calculator with 14 loaded.
2
Read the STEPS panel to see the reasoning: the smallest prime divisor of 14 is 2, which is enough to settle it, and the full factorisation 2 × 7 follows.
3
Check the six tiles for the derived quantities — divisor count, divisor sum, Euler's totient and the primes either side. All of them come from the factorisation rather than from separate searches.
4
Type a different number to carry on, or switch to RANGE to sieve a whole interval at once and see how the primes thin out as the numbers grow.

THE FORMULAS

Primeexactly two divisors: 1 and n

Trial division limittest primes up to √n only

Fundamental theoremn = p₁^a¹ × p₂^a² × … uniquely

Number of divisorsd(n) = Π (aᵢ + 1)

Sum of divisorsσ(n) = Π (pᵢ^(aᵢ+1) − 1)/(pᵢ − 1)

Euler totientφ(n) = n · Π (1 − 1/pᵢ)

Totient of a primeφ(p) = p − 1

Sieve pass startbegin each pass at p²

Prime Number Theoremπ(x) ≈ x ÷ ln x

Twin primesp and p + 2 both prime

Mersenne prime2^p − 1, with p itself prime

Perfect numberσ(n) − n = n

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Last updated: July 28, 2026 · Formula verified · Deterministic Miller–Rabin, so a result of PRIME is proven rather than probable · Eagle-eyed accuracy for every calculation.

Is 14 a Prime Number?

YOUR NUMBER

HOW TO USE

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