Factorial worksheet

1. 9!: 362,880

1. Write out the rule: n! (said "n factorial") means multiply every whole number from your number n down to 1

   $n\text{!}$$=\text{n × (n − 1) × … × 2 × 1}$

2. Multiply every whole number from 9 down to 1

   $9\text{!}$$=9\times 8\times 7\times \text{…}\times 1$$=\mathrm{362,880}$

3. Count the digits to get a feel for the size: the exact answer has 6 digits

   $\text{digits}$$=6$

4. Count the zeros at the end (Z). Each one needs a 2 and a 5, and 5s are rarer, so count multiples of 5, then 25, then 125

   $Z$$=\text{⌊}\frac{9}{5}\text{⌋}$$=1$

2. 11!: 39,916,800

1. Write out the rule: n! (said "n factorial") means multiply every whole number from your number n down to 1

   $n\text{!}$$=\text{n × (n − 1) × … × 2 × 1}$

2. Multiply every whole number from 11 down to 1

   $11\text{!}$$=11\times 10\times 9\times \text{…}\times 1$$=\mathrm{39,916,800}$

3. Count the digits to get a feel for the size: the exact answer has 8 digits

   $\text{digits}$$=8$

4. Count the zeros at the end (Z). Each one needs a 2 and a 5, and 5s are rarer, so count multiples of 5, then 25, then 125

   $Z$$=\text{⌊}\frac{11}{5}\text{⌋}$$=2$

3. 12!: 479,001,600

1. Write out the rule: n! (said "n factorial") means multiply every whole number from your number n down to 1

   $n\text{!}$$=\text{n × (n − 1) × … × 2 × 1}$

2. Multiply every whole number from 12 down to 1

   $12\text{!}$$=12\times 11\times 10\times \text{…}\times 1$$=\mathrm{479,001,600}$

3. Count the digits to get a feel for the size: the exact answer has 9 digits

   $\text{digits}$$=9$

4. Count the zeros at the end (Z). Each one needs a 2 and a 5, and 5s are rarer, so count multiples of 5, then 25, then 125

   $Z$$=\text{⌊}\frac{12}{5}\text{⌋}$$=2$

4. 8!: 40,320

1. Write out the rule: n! (said "n factorial") means multiply every whole number from your number n down to 1

   $n\text{!}$$=\text{n × (n − 1) × … × 2 × 1}$

2. Multiply every whole number from 8 down to 1

   $8\text{!}$$=8\times 7\times 6\times 5\times 4\times 3\times 2\times 1$$=\mathrm{40,320}$

3. Count the digits to get a feel for the size: the exact answer has 5 digits

   $\text{digits}$$=5$

4. Count the zeros at the end (Z). Each one needs a 2 and a 5, and 5s are rarer, so count multiples of 5, then 25, then 125

   $Z$$=\text{⌊}\frac{8}{5}\text{⌋}$$=1$

5. 7!: 5,040

1. Write out the rule: n! (said "n factorial") means multiply every whole number from your number n down to 1

   $n\text{!}$$=\text{n × (n − 1) × … × 2 × 1}$

2. Multiply every whole number from 7 down to 1

   $7\text{!}$$=7\times 6\times 5\times 4\times 3\times 2\times 1$$=\mathrm{5,040}$

3. Count the digits to get a feel for the size: the exact answer has 4 digits

   $\text{digits}$$=4$

4. Count the zeros at the end (Z). Each one needs a 2 and a 5, and 5s are rarer, so count multiples of 5, then 25, then 125

   $Z$$=\text{⌊}\frac{7}{5}\text{⌋}$$=1$

6. 10!: 3,628,800

1. Write out the rule: n! (said "n factorial") means multiply every whole number from your number n down to 1

   $n\text{!}$$=\text{n × (n − 1) × … × 2 × 1}$

2. Multiply every whole number from 10 down to 1

   $10\text{!}$$=10\times 9\times 8\times \text{…}\times 1$$=\mathrm{3,628,800}$

3. Count the digits to get a feel for the size: the exact answer has 7 digits

   $\text{digits}$$=7$

4. Count the zeros at the end (Z). Each one needs a 2 and a 5, and 5s are rarer, so count multiples of 5, then 25, then 125

   $Z$$=\text{⌊}\frac{10}{5}\text{⌋}$$=2$

7. 26!: 4.032914611 × 10^26

1. Write out the rule: n! (said "n factorial") means multiply every whole number from your number n down to 1

   $n\text{!}$$=\text{n × (n − 1) × … × 2 × 1}$

2. Multiply every whole number from 26 down to 1

   $26\text{!}$$=26\times 25\times 24\times \text{…}\times 1$$=\text{4.032914611 × 10^26}$

3. Count the digits to get a feel for the size: the exact answer has 27 digits

   $\text{digits}$$=27$

4. Count the zeros at the end (Z). Each one needs a 2 and a 5, and 5s are rarer, so count multiples of 5, then 25, then 125

   $Z$$=\text{⌊}\frac{26}{5}\text{⌋}+\text{⌊}\frac{26}{25}\text{⌋}$$=5+1$$=6$

8. 16!: 20,922,789,888,000

1. Write out the rule: n! (said "n factorial") means multiply every whole number from your number n down to 1

   $n\text{!}$$=\text{n × (n − 1) × … × 2 × 1}$

2. Multiply every whole number from 16 down to 1

   $16\text{!}$$=16\times 15\times 14\times \text{…}\times 1$$=\mathrm{20,922,789,888,000}$

3. Count the digits to get a feel for the size: the exact answer has 14 digits

   $\text{digits}$$=14$

4. Count the zeros at the end (Z). Each one needs a 2 and a 5, and 5s are rarer, so count multiples of 5, then 25, then 125

   $Z$$=\text{⌊}\frac{16}{5}\text{⌋}$$=3$

9. 18!: 6.402373706 × 10^15

1. Write out the rule: n! (said "n factorial") means multiply every whole number from your number n down to 1

   $n\text{!}$$=\text{n × (n − 1) × … × 2 × 1}$

2. Multiply every whole number from 18 down to 1

   $18\text{!}$$=18\times 17\times 16\times \text{…}\times 1$$=\text{6.402373706 × 10^15}$

3. Count the digits to get a feel for the size: the exact answer has 16 digits

   $\text{digits}$$=16$

4. Count the zeros at the end (Z). Each one needs a 2 and a 5, and 5s are rarer, so count multiples of 5, then 25, then 125

   $Z$$=\text{⌊}\frac{18}{5}\text{⌋}$$=3$

10. 14!: 87,178,291,200

1. Write out the rule: n! (said "n factorial") means multiply every whole number from your number n down to 1

   $n\text{!}$$=\text{n × (n − 1) × … × 2 × 1}$

2. Multiply every whole number from 14 down to 1

   $14\text{!}$$=14\times 13\times 12\times \text{…}\times 1$$=\mathrm{87,178,291,200}$

3. Count the digits to get a feel for the size: the exact answer has 11 digits

   $\text{digits}$$=11$

4. Count the zeros at the end (Z). Each one needs a 2 and a 5, and 5s are rarer, so count multiples of 5, then 25, then 125

   $Z$$=\text{⌊}\frac{14}{5}\text{⌋}$$=2$