# 1148 and Level 1

This level 1 puzzle has only one solution, and I’m sure you can find it. Just write the numbers from 1 to 10 in both the first column and the top row so that the clues and those numbers make a valid multiplication table. Print the puzzles or type the solution in this excel file: 10-factors-1148-1160

Now here’s some information about the number 1148:

• 1148 is a composite number.
• Prime factorization: 1148 = 2 × 2 × 7 × 41, which can be written 1148 = 2² × 7 × 41
• The exponents in the prime factorization are 2, 1, and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1)(1 + 1) = 3 × 2 × 2 = 12. Therefore 1148 has exactly 12 factors.
• Factors of 1148: 1, 2, 4, 7, 14, 28, 41, 82, 164, 287, 574, 1148
• Factor pairs: 1148 = 1 × 1148, 2 × 574, 4 × 287, 7 × 164, 14 × 82, or 28 × 41
• Taking the factor pair with the largest square number factor, we get √1148 = (√4)(√287) = 2√287 ≈ 33.88215 1148 is the sum of two consecutive primes:
571 + 577 = 1148

1148 is the hypotenuse of a Pythagorean triple:
252-1120-1148 which is 28 times (9-40-41)

1148 looks interesting to be in these other bases:
It’s 1120112 in BASE 3 because 3⁶ + 3⁵ + 2(3⁴) + 3² + 3¹ + 2(3⁰) = 1148,
1515 in BASE 9 because 9³ + 5(9²) + 9 + 5(1) = 1148,
and 161 in BASE 31 because 31² + 6(31) + 1 = 1148

This site uses Akismet to reduce spam. Learn how your comment data is processed.