(1, 5040)
(2, 2520)
(3, 1680)
(4, 1260)
(5, 1008)
(6, 840)
(7, 720)
(8, 630)
(9, 560)
(10, 504)
(12, 420)
(14, 360)
(15, 336)
(16, 315)
(18, 280)
(20, 252)
(21, 240)
(24, 210)
(28, 180)
(30, 168)
(35, 144)
(36, 140)
(40, 126)
(42, 120)
(45, 112)
(48, 105)
(56, 90)
(60, 84)
(63, 80)
(70, 72)
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(Here is one possible factor tree. Others may be different, but will have the same result.)
5040
2 x 2520
2 x 2 x 1260
2 x 2 x 2 x 630
2 x 2 x 2 x 2 x 315
2 x 2 x 2 x 2 x 3 x 105
2 x 2 x 2 x 2 x 3 x 3 x 35
2 x 2 x 2 x 2 x 3 x 3 x 5 x 7
(The last line can be written as 24 x 32 x 5 x 7)
express 5610 as the product of prime factors
5 x 7 = 35
As a product of its prime factors: 2*3*3*3*5 = 270
That's the prime factorization.
All composite numbers can be expressed as unique products of prime numbers. This is accomplished by dividing the original number and its factors by prime numbers until all the factors are prime. A factor tree can help you visualize this. Example: 210 210 Divide by two. 105,2 Divide by three. 35,3,2 Divide by five. 7,5,3,2 Stop. All the factors are prime. 2 x 3 x 5 x 7 = 210 That's the prime factorization of 210.