# 1525 Challenge Puzzle

Contents

### Today’s puzzle:

There is plenty to challenge you in solving this puzzle, but there are also quite a few very helpful clues. Just remember to use logic and have fun with it! Print the puzzles or type the solution in this excel file: 12 Factors 1511-1525

### Factors of 1525:

• 1525 is a composite number.
• Prime factorization: 1525 = 5 × 5 × 61, which can be written 1525 = 5² × 61.
• 1525 has at least one exponent greater than 1 in its prime factorization so √1525 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1525 = (√25)(√61) = 5√61.
• The exponents in the prime factorization are 2 and 1. Adding one to each exponent and multiplying we get (2 + 1)(1 + 1) = 3 × 2 = 6. Therefore 1525 has exactly 6 factors.
• The factors of 1525 are outlined with their factor pair partners in the graphic below. ### More about the Number 1525:

1525 is the sum of two squares in two different ways:
39² + 2² = 1525
38² + 9² = 1525

1525 is the hypotenuse of a Pythagorean triple in SEVEN different ways!
156-1517-1525, calculated from 2(39)( 2), 39² – 2², 39² + 2²,
275-1500-1525, which is 25 times (11-60-61),
427-1464-1525, which is (7-24-25) times 61,
680-1365-1525, which is 5 times (136-273-305)
684-1363-1525, calculated from 2(38)( 9), 38² – 9², 38² + 9²,
915-1220-1525, which is (3-4-5) times 305, and
1035-1120-1525, which is 5 times (207-224-305).

1525 is also the difference of two squares in two different ways:
763² – 762² = 1525,
155² – 150² = 1525, and
43² – 18² = 1525.

1525 is the 25th heptagonal number because
(5(25²)-3(25))/2 = 1525.
That means you can make a 7-sided figure out of 1525 dots where two of the sides are shared with all the previous heptagons.

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