# 1122 Factor Trees

We can easily tell that 1122 is divisible by 2 because it is even.
It is divisible by 3 because 1 + 2 = 3, no matter how many times you do it.
11 and 22 are both divisible by 11, so obviously, 1122 is as well.
1122 is also divisible by 17, but there isn’t an easy trick to use to find that out without just dividing it.

There are 24 ways to arrange the four factors of 1122. Each of those 24 ways can be the bottom four numbers of a factor tree (See the first three trees below.) or the numbers running down the side of a factor tree (See the last four trees below.). 1122 makes some very well proportioned factor trees!

• 1122 is a composite number.
• Prime factorization: 1122 = 2 × 3 × 11 × 17
• The exponents in the prime factorization are 1, 1, 1, and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 × 2 = 16. Therefore 1122 has exactly 16 factors.
• Factors of 1122: 1, 2, 3, 6, 11, 17, 22, 33, 34, 51, 66, 102, 187, 374, 561, 1122
• Factor pairs: 1122 = 1 × 1122, 2 × 561, 3 × 374, 6 × 187, 11 × 102, 17 × 66, 22 × 51, or 33 × 34
• 1122 has no square factors that allow its square root to be simplified. √1122 ≈ 33.49627 1122 is the product of two consecutive number: 33 × 34 = 1122
That makes 1122 the sum of the first 33 even numbers:
2 + 4 + 6 + 8 + . . . + 62 + 64 + 66 = 1122

1122 is the hypotenuse of a Pythagorean triple:
528-990-1122 which is (8-15-17) times 66

1122 is palindrome 2G2 in BASE 20 (G is 16 base 10)
because 2(20²) + 16(20) + 2(1) = 1122

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