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Considering the remainder "modulo" an integer is a powerful, foundational tool in Number Theory. You already use in clocks and work modulo 12.

If all integers are colored in the same pattern as the numbers in this grid, what color is 1234?

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If you **multiply** a blue number by an orange number, what color will the product be?

**Note:** Assume that *all* integers are colored according to the same pattern as the numbers in the grid.

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If you **add** a blue number to a yellow number, what color will the sum be?

**Note:** Assume that *all* integers are colored according to the same pattern as the numbers in the grid.

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If you **multiply** a green number by a yellow number, what color will the product be?

**Note:** Assume that *all* integers are colored according to the same pattern as the numbers in the grid.

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What color is \(8 \times 17 \, ?\)

**Note:** Assume that *all* integers are colored according to the same pattern as the numbers in the grid.

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