Today’s Puzzle:

A few days ago I published a new kind of factoring puzzle. Jo Morgan of Resourceaholic.com, keeps an eye out for new mathematical resources on Twitter. She was one of the first to notice and like my puzzle. Because of her, lots of other people noticed the puzzle, too. Today is Jo’s birthday, and I decided to make a similar puzzle for her to enjoy. You might find it slightly more difficult than the earlier puzzle, but use logic from the beginning, and you will be able to fit in all the factors.

Factors of 1708:

• 1708 is a composite number.
• Prime factorization: 1708 = 2 × 2 × 7 × 61, which can be written 1708 = 2² × 7 × 61.
• 1708 has at least one exponent greater than 1 in its prime factorization so √1708 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1708 = (√4)(√427) = 2√427.
• The exponents in the prime factorization are 2, 1, and 1. Adding one to each exponent and multiplying we get (2 + 1)(1 + 1)(1 + 1) = 3 × 2 × 2 = 12. Therefore 1708 has exactly 12 factors.
• The factors of 1708 are outlined with their factor pair partners in the graphic below.

More About the Number 1708:

1708 is the hypotenuse of a Pythagorean triple:
308-1680-1708, which is 28 times (11-60-61).