# Finding Number of Zeros in a Number

Concepts
Examples

To find the number of zeros at the end of a factorial or a product, **find the highest
power of 2 and 5 in the factorial or the product, number of zeros will be decided by the limiting factor**. (
one who's power is smaller will be the limiting factor)

**Limiting factor is the one who's power is less among 2 and 5**

**e.g. Finding number of Zeros in 150**

150 = 2 × 3 × 5 × 5,

∴ Highest power of 2 = 1

∴ Highest power of 5 = 2

∴ Limiting factor = 1

∴ Number of zeros in 150 = 1

**e.g. Finding number of Zeros in 10!**

∴ Highest power of 2 = 8

∴ Highest power of 5 = 2

∴ Limiting factor = 2

∴ Number of zeros in 10! = 2

**Question 1**Find the number of zeros at the end of 33 × 128 × 125 × 50 × 45

3 | 4 |

5 | 6 |

**Question 2**Find the number of zeros at the end of 100!

97 | 56 |

24 | 23 |

**Question 3**Find the number of zeros at the end of 125!

119 | 31 |

27 | 29 |

**Question 4**Find the number of zeros at the end of 390625 × 1024

8 | 10 |

15 | 17 |