Factors of 1225 are the list of integers that we can split evenly into 1225. There are total 9 factors of 1225 i.e. 1, 5, 7, 25, 35, 49, 175, 245, 1225. The sum of all factors of 1225 is 1767 and its factors in Pairs are (1, 1225), (5, 245), (7, 175), (25, 49), (35, 35).

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**All Factors of 1225:** 1, 5, 7, 25, 35, 49, 175, 245 and 1225 **Negative Factors of 1225:** -1, -5, -7, -25, -35, -49, -175, -245 and -1225 **Prime Factors of 1225:** 5, 7 **Prime Factorization of 1225:** 52 × 72 **Sum of Factors of 1225:** 1767

1. | What Are the Factors of 1225? |

2. | Factors of 1225 by Prime Factorization |

3. | Factors of 1225 in Pairs |

4. | FAQs on Factors of 1225 |

## What are Factors of 1225?

Factors of 1225 are pairs of those numbers whose products result in 1225. These factors are either prime numbers or composite numbers.

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### How to Find the Factors of 1225?

To find the factors of 1225, we will have to find the list of numbers that would divide 1225 without leaving any remainder.

1225/1225 = 1; therefore, 1225 is a factor of 1225.1225/245 = 5; therefore, 245 is a factor of 1225. Similarly we can find other factors. Hence, the factors of 1225 are 1, 5, 7, 25, 35, 49, 175, 245, 1225.

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## Factors of 1225 by Prime Factorization

The number 1225 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1225. The first step is to divide the number 1225 with the smallest prime factor, here it is 5. We keep dividing until it gives a non-zero remainder. 1225 ÷ 5 = 245 245 ÷ 5 = 49

Further dividing 49 by 5 gives a non-zero remainder. So we stop the process and continue dividing the number 49 by the next smallest prime factor. We stop ultimately if the next prime factor doesn”t exist or when we can”t divide any further.

So, the prime factorization of 1225 can be written as 52 × 72 where 5, 7 are prime.

## Factors of 1225 in Pairs

Pair factors of 1225 are the pairs of numbers that when multiplied give the product 1225. The factors of 1225 in pairs are:

1 × 1225 = (1, 1225) 5 × 245 = (5, 245) 7 × 175 = (7, 175) 25 × 49 = (25, 49) 35 × 35 = (35, 35)

Negative pair factors of 1225 are:

-1 × -1225 = (-1, -1225) -5 × -245 = (-5, -245) -7 × -175 = (-7, -175) -25 × -49 = (-25, -49) -35 × -35 = (-35, -35)

**NOTE:** If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.

## Factors of 1225 Solved Examples

**Example 1: How many factors are there for 1225?**

**Solution:**

The factors of 1225 are too many, therefore if we can find the prime factorization of 1225, then the total number of factors can be calculated using the formula shown below. If the prime factorization of the number is ax × by × cz where a, b, c are prime, then the total number of factors can be given by (x + 1)(y + 1)(z + 1). Prime Factorization of 1225 = 52 × 72 Therefore, the total number of factors are (2 + 1) × (2 + 1) = 3 × 3 = 9

** Example 3: Find if 1, 7, 35, 400 and 1225 are factors of 1225.**

**Solution:**

When we divide 1225 by 400 it leaves a remainder. Therefore, the number 400 is not a factor of 1225. All numbers except 400 are factors of 1225.

** Example 4: Find the product of all the prime factors of 1225.**

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**Solution:**

Since, the prime factors of 1225 are 5, 7. Therefore, the product of prime factors = 5 × 7 = 35.

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## FAQs on Factors of 1225

### What are the Factors of 1225?

The factors of 1225 are 1, 5, 7, 25, 35, 49, 175, 245, 1225 and its negative factors are -1, -5, -7, -25, -35, -49, -175, -245, -1225.

### What is the Sum of Factors of 1225?

Sum of all factors of 1225 = (52 + 1 – 1)/(5 – 1) × (72 + 1 – 1)/(7 – 1) = 1767

### What are the Pair Factors of 1225?

The pair factors of 1225 are (1, 1225), (5, 245), (7, 175), (25, 49), (35, 35).

### What is the Greatest Common Factor of 1225 and 839?

The factors of 1225 are 1, 5, 7, 25, 35, 49, 175, 245, 1225 and the factors of 839 are 1, 839. 1225 and 839 have only one common factor which is 1. This implies that 1225 and 839 are co-prime. Hence, the Greatest Common Factor (GCF) of 1225 and 839 is 1.

### How Many Factors of 1225 are also common to the Factors of 264?

Since, the factors of 1225 are 1, 5, 7, 25, 35, 49, 175, 245, 1225 and factors of 264 are 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, 264. Hence, 1225 and 264 have only one common factor which is 1. Therefore, 1225 and 264 are co-prime.

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