# 1348 Coloring Paula Krieg’s Polar Rose

Paula Beardell Krieg recently wrote about using Desmos to create designs that can be colored by hand or by computer programs like Paint. I like using Paint so with her permission I took a design she made and colored it so I could present it here in this post. I chose colors that make me think of spring because, frankly, I’m ready for winter to be over!

Now I’ll write a little bit about the number 1348:

• 1348 is a composite number.
• Prime factorization: 1348 = 2 × 2 × 337, which can be written 1348 = 2² × 337
• 1348 has at least one exponent greater than 1 in its prime factorization so √1348 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1348 = (√4)(√337) = 2√337
• 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 1348 has exactly 6 factors.
• The factors of 1348 are outlined with their factor pair partners in the graphic below.

1348 is the sum of two squares:
32² + 18² = 1348

1348 is the hypotenuse of a Pythagorean triple:
700-1152-1348 which is 32² – 18², 2(32)(18), 32² + 18²

1348 is also the short leg in a primitive Pythagorean triple:
1348-454275-454277