Factors of 780
Factors of 780 are the list of integers that we can split evenly into 780. There are overall 24 factors of 780, of which 2, 3, 5, 13 are its prime factors. The sum of all factors of 780 is 2352.
- All Factors of 780: 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390 and 780
- Prime Factors of 780: 2, 3, 5, 13
- Prime Factorization of 780: 22 × 31 × 51 × 131
- Sum of Factors of 780: 2352
1. | What Are the Factors of 780? |
2. | Factors of 780 by Prime Factorization |
3. | Factors of 780 in Pairs |
4. | FAQs on Factors of 780 |
What are Factors of 780?
Factors of 780 are pairs of those numbers whose products result in 780. These factors are either prime numbers or composite numbers.
How to Find the Factors of 780?
To find the factors of 780, we will have to find the list of numbers that would divide 780 without leaving any remainder.
- 780/15 = 52; therefore, 15 is a factor of 780 and 52 is also a factor of 780.
- 780/26 = 30; therefore, 26 is a factor of 780 and 30 is also a factor of 780.
☛ Also Check:
- Factors of 49 - The factors of 49 are 1, 7, 49
- Factors of 40 - The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
- Factors of 72 - The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
- Factors of 39 - The factors of 39 are 1, 3, 13, 39
- Factors of 66 - The factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66
Factors of 780 by Prime Factorization
- 780 ÷ 2 = 390
- 390 ÷ 2 = 195
Further dividing 195 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 195 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 780 can be written as 22 × 31 × 51 × 131 where 2, 3, 5, 13 are prime.
Factors of 780 in Pairs
Pair factors of 780 are the pairs of numbers that when multiplied give the product 780. The factors of 780 in pairs are:
- 1 × 780 = (1, 780)
- 2 × 390 = (2, 390)
- 3 × 260 = (3, 260)
- 4 × 195 = (4, 195)
- 5 × 156 = (5, 156)
- 6 × 130 = (6, 130)
- 10 × 78 = (10, 78)
- 12 × 65 = (12, 65)
- 13 × 60 = (13, 60)
- 15 × 52 = (15, 52)
- 20 × 39 = (20, 39)
- 26 × 30 = (26, 30)
Negative pair factors of 780 are:
- -1 × -780 = (-1, -780)
- -2 × -390 = (-2, -390)
- -3 × -260 = (-3, -260)
- -4 × -195 = (-4, -195)
- -5 × -156 = (-5, -156)
- -6 × -130 = (-6, -130)
- -10 × -78 = (-10, -78)
- -12 × -65 = (-12, -65)
- -13 × -60 = (-13, -60)
- -15 × -52 = (-15, -52)
- -20 × -39 = (-20, -39)
- -26 × -30 = (-26, -30)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 780 Solved Examples
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Example 1: How many factors are there for 780?
Solution:
The factors of 780 are too many, therefore if we can find the prime factorization of 780, 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 780 = 22 × 31 × 51 × 131
Therefore, the total number of factors are (2 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 3 × 2 × 2 × 2 = 24 -
Example 2: Find the Least Common Multiple and Greatest Common Divisor (GCD) of 780 and 415.
Solution:
The factors of 780 are 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390, 780 and factors of 415 are 1, 5, 83, 415.
Therefore, the Least Common Multiple of 780 and 415 is 64740 and Greatest Common Divisor (GCD) of 780 and 415 is 5. -
Example 3: Find if 2, 10, 13, 39, 60, 130, 390 and 495 are factors of 780.
Solution:
When we divide 780 by 495 it leaves a remainder. Therefore, the number 495 is not a factor of 780. All numbers except 495 are factors of 780.
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Example 4: Find the product of all the prime factors of 780.
Solution:
Since, the prime factors of 780 are 2, 3, 5, 13. Therefore, the product of prime factors = 2 × 3 × 5 × 13 = 390.
FAQs on Factors of 780
What are the Factors of 780?
The factors of 780 are 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390, 780 and its negative factors are -1, -2, -3, -4, -5, -6, -10, -12, -13, -15, -20, -26, -30, -39, -52, -60, -65, -78, -130, -156, -195, -260, -390, -780.
What is the Sum of all Factors of 780?
Sum of all factors of 780 = (22 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) × (51 + 1 - 1)/(5 - 1) × (131 + 1 - 1)/(13 - 1) = 2352
What are the Pair Factors of 780?
The pair factors of 780 are (1, 780), (2, 390), (3, 260), (4, 195), (5, 156), (6, 130), (10, 78), (12, 65), (13, 60), (15, 52), (20, 39), (26, 30).
What is the Greatest Common Factor of 780 and 762?
The factors of 780 and 762 are 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390, 780 and 1, 2, 3, 6, 127, 254, 381, 762 respectively.
Common factors of 780 and 762 are [1, 2, 3, 6].
Hence, the Greatest Common Factor of 780 and 762 is 6.
How Many Factors of 780 are also common to the Factors of 289?
Since, the factors of 780 are 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390, 780 and factors of 289 are 1, 17, 289. Hence, 780 and 289 have only one common factor which is 1. Therefore, 780 and 289 are co-prime.
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