Common Factors Cards C8864C

1. **State the problem:** Malik has 6 rare cards and 15 standard cards. He wants to divide them into equal groups so that each friend gets the same number of rare cards and the same number of standard cards. 2. **Find all factors of 6 (for rare cards):** Factors are numbers that divide 6 without remainder. $$6 = 1 \times 6 = 2 \times 3$$ So, the factors of 6 are: $1, 2, 3, 6$ 3. **Find all factors of 15 (for standard cards):** Factors are numbers that divide 15 without remainder. $$15 = 1 \times 15 = 3 \times 5$$ So, the factors of 15 are: $1, 3, 5, 15$ 4. **List all ways Malik can put the 6 rare cards into equal groups:** He can make $1, 2, 3,$ or $6$ groups. 5. **List all ways Malik can put the 15 standard cards into equal groups:** He can make $1, 3, 5,$ or $15$ groups. 6. **Find how many friends Malik can give cards to so that all cards are given away:** He must find the common factors of 6 and 15 because the number of friends must divide both 6 and 15 exactly. 7. **Find common factors of 6 and 15:** Factors of 6: $1, 2, 3, 6$ Factors of 15: $1, 3, 5, 15$ Common factors: $1, 3$ 8. **Malik can give cards to either $1$ or $3$ friends so that all cards are distributed equally without leftovers.** 9. **Relation to factors:** The answer to 2c is the common factors of 6 and 15. This means the number of friends must be a factor of both numbers to divide the cards equally. **Final answers:** - a. $1, 2, 3, 6$ - b. $1, 3, 5, 15$ - c. $1$ or $3$ friends - d. The number of friends is a common factor of 6 and 15, ensuring equal division of both types of cards.