The number of zeros at the end of the product of all the prime numbers between 1 and 1111 is :

Options

A. 222
B. 21
C. can't be determined
D. none of these

Answer

To find the number of zeros at the end of the product of all the prime numbers between 1 and 1111, we need to understand how zeros are formed in a number. A zero is formed by the factors 10, which is the product of 2 and 5. Therefore, we need to count how many pairs of the factors 2 and 5 are present in the product of the prime numbers.

### Step-by-step Solution:

1. **Identify the Prime Numbers between 1 and 1111**:
The prime numbers between 1 and 1111 include: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1177, 1181, 1187, 1193, 1201, 1213, 1217, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1513, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111.

2. **Count the Factors of 2 and 5**:
- The only even prime number is 2.
- The only prime number that is a multiple of 5 is 5.
- Therefore, in the product of all prime numbers, we have one factor of 2 (from the prime number 2) and one factor of 5 (from the prime number 5).

3. **Calculate the Number of Pairs of (2, 5)**:
- Since we have one factor of 2 and one factor of 5, we can form exactly one pair of (2, 5).
- Each pair of (2, 5) contributes one zero to the end of the product.

4. **Conclusion**:
- The total number of zeros at the end of the product of all prime numbers between 1 and 1111 is 1.

### Final Answer:
The number of zeros at the end of the product of all the prime numbers between 1 and 1111 is **1**.