### 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.