# 1480 and Level 3

Contents

### Today’s Puzzle:

This is a level 3 puzzle. Start with the common factor of 21 and 14, then fill in the cells in the first column in order from top to bottom as well as the factors in the top row until you have placed all of the factors from 1 to 10 in both of those places. ### Factors of 1480:

80 is divisible by 8 and 4 is even, so 1480 is divisible by 8. Here’s a little more about its factors:

• 1480 is a composite number.
• Prime factorization: 1480 = 2 × 2 × 2 × 5 × 37, which can be written 1480 = 2³ × 5 × 37
• 1480 has at least one exponent greater than 1 in its prime factorization so √1480 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1480 = (√4)(√370) = 2√370
• The exponents in the prime factorization are 3,1 and 1. Adding one to each exponent and multiplying we get (3 + 1)(1 + 1) (1 + 1) = 4 × 2 × 2 = 16. Therefore 1480 has exactly 16 factors.
• The factors of 1480 are outlined with their factor pair partners in the graphic below. ### Something else about the number 1480:

1480 is the hypotenuse of FOUR Pythagorean triples:
456-1408-1480 which is 8 times (57-176-185)
480-1400-1480 which is (12-35-37) times 40
832-1224-1480 which is 8 times (104-153-185)
888-1184-1480 which is (3-4-5) times 296

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