Factors of 2916
Factors of 2916 are integers that can be divided evenly into 2916. There are overall 21 factors of 2916 among which 2916 is the biggest factor and its prime factors are 2, 3. The sum of all factors of 2916 is 7651.
- All Factors of 2916: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 729, 972, 1458 and 2916
- Prime Factors of 2916: 2, 3
- Prime Factorization of 2916: 22 × 36
- Sum of Factors of 2916: 7651
1. | What Are the Factors of 2916? |
2. | Factors of 2916 by Prime Factorization |
3. | Factors of 2916 in Pairs |
4. | FAQs on Factors of 2916 |
What are Factors of 2916?
Factors of 2916 are pairs of those numbers whose products result in 2916. These factors are either prime numbers or composite numbers.
How to Find the Factors of 2916?
To find the factors of 2916, we will have to find the list of numbers that would divide 2916 without leaving any remainder.
- 2916/6 = 486; therefore, 6 is a factor of 2916 and 486 is also a factor of 2916.
- 2916/324 = 9; therefore, 324 is a factor of 2916 and 9 is also a factor of 2916.
☛ Also Check:
- Factors of 128 - The factors of 128 are 1, 2, 4, 8, 16, 32, 64, 128
- Factors of 78 - The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78
- Factors of 65 - The factors of 65 are 1, 5, 13, 65
- Factors of 144 - The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
- Factors of 72 - The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Factors of 2916 by Prime Factorization
- 2916 ÷ 2 = 1458
- 1458 ÷ 2 = 729
Further dividing 729 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 729 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 2916 can be written as 22 × 36 where 2, 3 are prime.
Factors of 2916 in Pairs
Pair factors of 2916 are the pairs of numbers that when multiplied give the product 2916. The factors of 2916 in pairs are:
- 1 × 2916 = (1, 2916)
- 2 × 1458 = (2, 1458)
- 3 × 972 = (3, 972)
- 4 × 729 = (4, 729)
- 6 × 486 = (6, 486)
- 9 × 324 = (9, 324)
- 12 × 243 = (12, 243)
- 18 × 162 = (18, 162)
- 27 × 108 = (27, 108)
- 36 × 81 = (36, 81)
- 54 × 54 = (54, 54)
Negative pair factors of 2916 are:
- -1 × -2916 = (-1, -2916)
- -2 × -1458 = (-2, -1458)
- -3 × -972 = (-3, -972)
- -4 × -729 = (-4, -729)
- -6 × -486 = (-6, -486)
- -9 × -324 = (-9, -324)
- -12 × -243 = (-12, -243)
- -18 × -162 = (-18, -162)
- -27 × -108 = (-27, -108)
- -36 × -81 = (-36, -81)
- -54 × -54 = (-54, -54)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 2916 Solved Examples
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Example 1: How many factors are there for 2916?
Solution:
The factors of 2916 are too many, therefore if we can find the prime factorization of 2916, 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 2916 = 22 × 36
Therefore, the total number of factors are (2 + 1) × (6 + 1) = 3 × 7 = 21 -
Example 2: Find the Lowest Common Multiple (LCM) and Highest Common Factor (HCF) of 2916 and 2873.
Solution:
The factors of 2916 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 729, 972, 1458, 2916 and factors of 2873 are 1, 13, 17, 169, 221, 2873.
Therefore, the Lowest Common Multiple (LCM) of 2916 and 2873 is 8377668 and Highest Common Factor (HCF) of 2916 and 2873 is 1. -
Example 3: Find if 12, 18, 54, 324, 486, 1458, 1746 and 2916 are factors of 2916.
Solution:
When we divide 2916 by 1746 it leaves a remainder. Therefore, the number 1746 is not a factor of 2916. All numbers except 1746 are factors of 2916.
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Example 4: Find the product of all the prime factors of 2916.
Solution:
Since, the prime factors of 2916 are 2, 3. Therefore, the product of prime factors = 2 × 3 = 6.
FAQs on Factors of 2916
What are the Factors of 2916?
The factors of 2916 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 729, 972, 1458, 2916 and its negative factors are -1, -2, -3, -4, -6, -9, -12, -18, -27, -36, -54, -81, -108, -162, -243, -324, -486, -729, -972, -1458, -2916.
What is the Sum of the Factors of 2916?
Sum of all factors of 2916 = (22 + 1 - 1)/(2 - 1) × (36 + 1 - 1)/(3 - 1) = 7651
What are the Pair Factors of 2916?
The pair factors of 2916 are (1, 2916), (2, 1458), (3, 972), (4, 729), (6, 486), (9, 324), (12, 243), (18, 162), (27, 108), (36, 81), (54, 54).
What is the Greatest Common Factor of 2916 and 1306?
The factors of 2916 and 1306 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 729, 972, 1458, 2916 and 1, 2, 653, 1306 respectively.
Common factors of 2916 and 1306 are [1, 2].
Hence, the GCF of 2916 and 1306 is 2.
How Many Factors of 2916 are also common to the Factors of 1865?
Since, the factors of 2916 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 729, 972, 1458, 2916 and factors of 1865 are 1, 5, 373, 1865. Hence, 2916 and 1865 have only one common factor which is 1. Therefore, 2916 and 1865 are co-prime.
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