1. **State the problem:** We want to find how to get the numbers 7, 21, 55, 56, and 64 from the number 147. 2. **Analyze the problem:** One common approach is to check if these numbers are factors or related by division or subtraction to 147. 3. **Check if each number divides 147:** - $\frac{147}{7} = 21$ - $\frac{147}{21} = 7$ - $\frac{147}{55} \approx 2.67$ (not an integer) - $\frac{147}{56} \approx 2.625$ (not an integer) - $\frac{147}{64} \approx 2.2969$ (not an integer) 4. **Check differences:** - $147 - 7 = 140$ - $147 - 21 = 126$ - $147 - 55 = 92$ - $147 - 56 = 91$ - $147 - 64 = 83$ No obvious pattern here. 5. **Check sums of pairs:** For example, $7 + 21 = 28$, $55 + 56 = 111$, $7 + 64 = 71$, no clear relation to 147. 6. **Check if these numbers are parts of a factorization or sum decomposition:** - $7 + 21 + 55 + 56 + 64 = 203$ which is greater than 147. 7. **Try to express 147 as a sum of some of these numbers:** - $7 + 21 + 55 + 56 = 139$ (close but not 147) - $7 + 21 + 64 = 92$ 8. **Try multiplication or other operations:** - $7 \times 21 = 147$ This is a key insight: $7 \times 21 = 147$. 9. **Conclusion:** The numbers 7 and 21 multiply to 147. The other numbers (55, 56, 64) do not directly relate by simple multiplication or division to 147. **Final answer:** The numbers 7 and 21 are factors of 147 since $$7 \times 21 = 147$$.