Today’s Puzzle:

Perhaps you can imagine that this level 4 puzzle looks like a couple of candy bars, one for you and one for me!

Factors of 1589:

Divisibility rules let us know quickly that 1589 is not divisible by 2, 3, or 5. Is it divisible by 7, the next prime number. We can apply the divisibility rule for 7 to find out:

1589 is divisible by 7 because
158 – 2(9) = 158 – 18 = 140, and 140 is divisible by 7.

• 1589 is a composite number.
• Prime factorization: 1589 = 7 × 227.
• 1589 has no exponents greater than 1 in its prime factorization, so √1589 cannot be simplified.
• The exponents in the prime factorization are 1 and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 1589 has exactly 4 factors.
• The factors of 1589 are outlined with their factor pair partners in the graphic below.

More about the Number 1589:

1589 is the difference of two squares two different ways:
795² – 794² = 1589, and
117² – 110² = 1589.

1589 is the sum of consecutive numbers in three different ways:
1589 is the sum of the two numbers from 794 to 795.
1589 is the sum of the seven numbers from 224 to 230.
1589 is also the sum of the fourteen numbers from 107 to 120,

 

When I was a child I remember eating a red-hot cinnamon ball around the holidays. I really like cinnamon, but I wasn’t sure I liked how hot the candy was. I hope you enjoy today’s red-hot cinnamon candy puzzle.

Print the puzzles or type the solution in this excel file: 12 factors 978-985

Now here’s something interesting about the number 982:

It is palindrome 292 in BASE 20 because 2(20²) + 9(20) + 2(1) = 982.

• 982 is a composite number.
• Prime factorization: 982 = 2 × 491
• The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 982 has exactly 4 factors.
• Factors of 982: 1, 2, 491, 982
• Factor pairs: 982 = 1 × 982 or 2 × 491
• 982 has no square factors that allow its square root to be simplified. √982 ≈ 31.336879