Thursday

Raven spreads the Field Day supplies across the workshop bench. "36 ribbons and 48 badges. Every kit must be the same."

"Thirty-six kits with one ribbon each," Rocket says. "Badges, um, one and a bit?"

"No leftovers, and no bits," says Raven. "What do you notice about the numbers 36 and 48?"

Rocket lists factors on the clipboard. "Both divide by 2, 3, 4, 6, and 12. Twelve is the biggest."

"Twelve kits," says Raven. "Three ribbons and four badges in each."

Nova hovers over two kitchen timers. "These beep every 6 seconds and every 8 seconds," she says. "When do they beep together?"

Rocket starts counting on his fingers. Nova hums. "Multiples, not factors, for that one."

A factor of a number divides it evenly. A common factor divides both numbers. The greatest common factor (GCF) is the biggest one.

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

On both lists: 1, 2, 3, 4, 6, 12. The GCF is 12, so the crew can pack 12 equal kits.

A multiple of a number is that number times 1, 2, 3 and so on. The least common multiple (LCM) is the smallest shared one.

Multiples of 6: 6, 12, 18, 24, 30. Multiples of 8: 8, 16, 24, 32.

The LCM of 6 and 8 is 24. The timers beep together every 24 seconds.

36 + 48 can be written as a multiple of a sum: 12 × (3 + 4). Twelve kits, each with 3 + 4 items.

The numbers inside the parentheses share no common factor. That is what makes the GCF the right number outside.

Kits packed. Tomorrow you spot decimals and common factors in everyday life, then review the week.