Factors of 1260 are integers that can be divided evenly into 1260. It has total 36 factors of which 1260 is the biggest factor and the prime factors of 1260 are 2, 3, 5, 7. The sum of all factors of 1260 is 4368.

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**All Factors of 1260:** 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 70, 84, 90, 105, 126, 140, 180, 210, 252, 315, 420, 630 and 1260 **Prime Factors of 1260:** 2, 3, 5, 7 **Prime Factorization of 1260:** 22 × 32 × 51 × 71 **Sum of Factors of 1260:** 4368

1. | What Are the Factors of 1260? |

2. | Factors of 1260 by Prime Factorization |

3. | Factors of 1260 in Pairs |

4. | FAQs on Factors of 1260 |

Factors of 1260 are pairs of those numbers whose products result in 1260. These factors are either prime numbers or composite numbers.

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### How to Find the Factors of 1260?

To find the factors of 1260, we will have to find the list of numbers that would divide 1260 without leaving any remainder.

1260/9 = 140; therefore, 9 is a factor of 1260 and 140 is also a factor of 1260.1260/210 = 6; therefore, 210 is a factor of 1260 and 6 is also a factor of 1260. Similarly we can find other factors. Hence, the factors of 1260 are 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 70, 84, 90, 105, 126, 140, 180, 210, 252, 315, 420, 630, 1260.

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The number 1260 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1260. The first step is to divide the number 1260 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder. 1260 ÷ 2 = 630 630 ÷ 2 = 315

Further dividing 315 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 315 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 1260 can be written as 22 × 32 × 51 × 71 where 2, 3, 5, 7 are prime.

Pair factors of 1260 are the pairs of numbers that when multiplied give the product 1260. The factors of 1260 in pairs are:

1 × 1260 = (1, 1260) 2 × 630 = (2, 630) 3 × 420 = (3, 420) 4 × 315 = (4, 315) 5 × 252 = (5, 252) 6 × 210 = (6, 210) 7 × 180 = (7, 180) 9 × 140 = (9, 140) 10 × 126 = (10, 126) 12 × 105 = (12, 105) 14 × 90 = (14, 90) 15 × 84 = (15, 84) 18 × 70 = (18, 70) 20 × 63 = (20, 63) 21 × 60 = (21, 60) 28 × 45 = (28, 45) 30 × 42 = (30, 42) 35 × 36 = (35, 36)

Negative pair factors of 1260 are:

-1 × -1260 = (-1, -1260) -2 × -630 = (-2, -630) -3 × -420 = (-3, -420) -4 × -315 = (-4, -315) -5 × -252 = (-5, -252) -6 × -210 = (-6, -210) -7 × -180 = (-7, -180) -9 × -140 = (-9, -140) -10 × -126 = (-10, -126) -12 × -105 = (-12, -105) -14 × -90 = (-14, -90) -15 × -84 = (-15, -84) -18 × -70 = (-18, -70) -20 × -63 = (-20, -63) -21 × -60 = (-21, -60) -28 × -45 = (-28, -45) -30 × -42 = (-30, -42) -35 × -36 = (-35, -36)

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

**Example 1: How many factors are there for 1260?**

**Solution:**

The factors of 1260 are too many, therefore if we can find the prime factorization of 1260, 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 1260 = 22 × 32 × 51 × 71 Therefore, the total number of factors are (2 + 1) × (2 + 1) × (1 + 1) × (1 + 1) = 3 × 3 × 2 × 2 = 36

** Example 3: Find if 5, 10, 14, 21, 105, 210, 420 and 1018 are factors of 1260.**

**Solution:**

When we divide 1260 by 1018 it leaves a remainder. Therefore, the number 1018 is not a factor of 1260. All numbers except 1018 are factors of 1260.

** Example 4: Find the product of all the prime factors of 1260.**

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**Solution:**

Since, the prime factors of 1260 are 2, 3, 5, 7. Therefore, the product of prime factors = 2 × 3 × 5 × 7 = 210.

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