Question 1

How do I find the prime factorization?

Accepted Answer

Divide repeatedly by the smallest prime that fits: 84 = 2×42 = 2×2×21 = 2²×3×7. Enter a number above to see it with exponents.

Question 2

How do I find the GCF?

Accepted Answer

Take the lower power of each shared prime: 12=2²×3 and 18=2×3² share 2×3, so GCF=6. The Euclidean algorithm gives the same result quickly.

Question 3

Is there an LCM formula?

Accepted Answer

For two numbers, LCM = a×b ÷ GCF. Example: 12 and 18 → 216÷6 = 36. For more numbers, fold them in pairwise.

Question 4

What counts as a prime?

Accepted Answer

A number ≥ 2 whose only divisors are 1 and itself. There are 25 primes up to 100, highlighted in the chart below.

n	factors	n	factors	n	factors	n	factors
2	prime	3	prime	4	2²	5	prime
6	2 × 3	7	prime	8	2³	9	3²
10	2 × 5	11	prime	12	2² × 3	13	prime
14	2 × 7	15	3 × 5	16	2⁴	17	prime
18	2 × 3²	19	prime	20	2² × 5	21	3 × 7
22	2 × 11	23	prime	24	2³ × 3	25	5²
26	2 × 13	27	3³	28	2² × 7	29	prime
30	2 × 3 × 5	31	prime	32	2⁵	33	3 × 11
34	2 × 17	35	5 × 7	36	2² × 3²	37	prime
38	2 × 19	39	3 × 13	40	2³ × 5	41	prime
42	2 × 3 × 7	43	prime	44	2² × 11	45	3² × 5
46	2 × 23	47	prime	48	2⁴ × 3	49	7²
50	2 × 5²	51	3 × 17	52	2² × 13	53	prime
54	2 × 3³	55	5 × 11	56	2³ × 7	57	3 × 19
58	2 × 29	59	prime	60	2² × 3 × 5	61	prime
62	2 × 31	63	3² × 7	64	2⁶	65	5 × 13
66	2 × 3 × 11	67	prime	68	2² × 17	69	3 × 23
70	2 × 5 × 7	71	prime	72	2³ × 3²	73	prime
74	2 × 37	75	3 × 5²	76	2² × 19	77	7 × 11
78	2 × 3 × 13	79	prime	80	2⁴ × 5	81	3⁴
82	2 × 41	83	prime	84	2² × 3 × 7	85	5 × 17
86	2 × 43	87	3 × 29	88	2³ × 11	89	prime
90	2 × 3² × 5	91	7 × 13	92	2² × 23	93	3 × 31
94	2 × 47	95	5 × 19	96	2⁵ × 3	97	prime
98	2 × 7²	99	3² × 11	100	2² × 5²	101	prime

Prime Factorization · GCF · LCM

Primes, GCF and LCM