Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 140, 160 i.e. 20 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 140 and 160 is **20**.

GCF(140,160) = 20

*Greatest common factor* or Greatest common divisor (GCD) can be calculated in following way;

- Greatest Common Factor of 140 and 160 by prime factorization method
- Greatest Common Factor of 140 and 160 by matching factors method

**Prime Factorization of 140**

2 | 140 |

2 | 70 |

5 | 35 |

7 | 7 |

1 |

Prime factors of 140 are 2,5,7. Prime factorization of **140** in exponential form is:

140 = 2^{2}×5^{1}×7^{1}

**Prime Factorization of 160**

2 | 160 |

2 | 80 |

2 | 40 |

2 | 20 |

2 | 10 |

5 | 5 |

1 |

Prime factors of 160 are 2,5. Prime factorization of **160** in exponential form is:

160 = 2^{5}×5^{1}

∴ So by taking common prime factors GCF of 140 and 160 is 20

**Factors of 140**

List of positive integer factors of 140 that divides 140 without a remainder.

1,2,4,5,7,10,14,20,28,35,70,140

**Factors of 160**

List of positive integer factors of 160 that divides 160 without a remainder.

1,2,4,5,8,10,16,20,32,40,80,160

**Greatest Common Factor**

We found the factors and prime factorization of 140 and 160. The biggest common factor number is the **GCF** number.

So the **greatest common factor 140 and 160** is **20**.

Also check out the Least Common Multiple of 140 and 160

(i) The GCF of 140 and 160 is associative

GCF of 140 and 160 = GCF of 160 and 140

1. What is the GCF of 140 and 160?

Answer: GCF of 140 and 160 is 20.

2. What are the Factors of 140?

Answer: Factors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140. There are 12 integers that are factors of 140. The greatest factor of 140 is 140.

3. What are the Factors of 160?

Answer: Factors of 160 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160. There are 12 integers that are factors of 160. The greatest factor of 160 is 160.

4. How to Find the GCF of 140 and 160?

Answer:

Greatest Common Factor of 140 and 160 = 20

Step 1: Find the prime factorization of 140

140 = 2 x 2 x 5 x 7

Step 2: Find the prime factorization of 160

160 = 2 x 2 x 2 x 2 x 2 x 5

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 2 x 2 x 5 = 20

Step 4: Therefore, the greatest common factor of 140 and 160 is 20