### 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:

**158****9** 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,