Factors of 2520
Factors of 2520 are the list of integers that we can split evenly into 2520. There are 48 factors of 2520 of which 2520 itself is the biggest factor and its prime factors are 2, 3, 5, 7 The sum of all factors of 2520 is 9360.
- All Factors of 2520: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 56, 60, 63, 70, 72, 84, 90, 105, 120, 126, 140, 168, 180, 210, 252, 280, 315, 360, 420, 504, 630, 840, 1260 and 2520
- Prime Factors of 2520: 2, 3, 5, 7
- Prime Factorization of 2520: 23 × 32 × 51 × 71
- Sum of Factors of 2520: 9360
1. | What Are the Factors of 2520? |
2. | Factors of 2520 by Prime Factorization |
3. | Factors of 2520 in Pairs |
4. | FAQs on Factors of 2520 |
What are Factors of 2520?
Factors of 2520 are pairs of those numbers whose products result in 2520. These factors are either prime numbers or composite numbers.
How to Find the Factors of 2520?
To find the factors of 2520, we will have to find the list of numbers that would divide 2520 without leaving any remainder.
- 2520/10 = 252; therefore, 10 is a factor of 2520 and 252 is also a factor of 2520.
- 2520/42 = 60; therefore, 42 is a factor of 2520 and 60 is also a factor of 2520.
☛ Also Check:
- Factors of 91 - The factors of 91 are 1, 7, 13, 91
- Factors of 52 - The factors of 52 are 1, 2, 4, 13, 26, 52
- Factors of 49 - The factors of 49 are 1, 7, 49
- Factors of 14 - The factors of 14 are 1, 2, 7, 14
- Factors of 17 - The factors of 17 are 1, 17
Factors of 2520 by Prime Factorization
- 2520 ÷ 2 = 1260
- 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 2520 can be written as 23 × 32 × 51 × 71 where 2, 3, 5, 7 are prime.
Factors of 2520 in Pairs
Pair factors of 2520 are the pairs of numbers that when multiplied give the product 2520. The factors of 2520 in pairs are:
- 1 × 2520 = (1, 2520)
- 2 × 1260 = (2, 1260)
- 3 × 840 = (3, 840)
- 4 × 630 = (4, 630)
- 5 × 504 = (5, 504)
- 6 × 420 = (6, 420)
- 7 × 360 = (7, 360)
- 8 × 315 = (8, 315)
- 9 × 280 = (9, 280)
- 10 × 252 = (10, 252)
- 12 × 210 = (12, 210)
- 14 × 180 = (14, 180)
- 15 × 168 = (15, 168)
- 18 × 140 = (18, 140)
- 20 × 126 = (20, 126)
- 21 × 120 = (21, 120)
- 24 × 105 = (24, 105)
- 28 × 90 = (28, 90)
- 30 × 84 = (30, 84)
- 35 × 72 = (35, 72)
- 36 × 70 = (36, 70)
- 40 × 63 = (40, 63)
- 42 × 60 = (42, 60)
- 45 × 56 = (45, 56)
Negative pair factors of 2520 are:
- -1 × -2520 = (-1, -2520)
- -2 × -1260 = (-2, -1260)
- -3 × -840 = (-3, -840)
- -4 × -630 = (-4, -630)
- -5 × -504 = (-5, -504)
- -6 × -420 = (-6, -420)
- -7 × -360 = (-7, -360)
- -8 × -315 = (-8, -315)
- -9 × -280 = (-9, -280)
- -10 × -252 = (-10, -252)
- -12 × -210 = (-12, -210)
- -14 × -180 = (-14, -180)
- -15 × -168 = (-15, -168)
- -18 × -140 = (-18, -140)
- -20 × -126 = (-20, -126)
- -21 × -120 = (-21, -120)
- -24 × -105 = (-24, -105)
- -28 × -90 = (-28, -90)
- -30 × -84 = (-30, -84)
- -35 × -72 = (-35, -72)
- -36 × -70 = (-36, -70)
- -40 × -63 = (-40, -63)
- -42 × -60 = (-42, -60)
- -45 × -56 = (-45, -56)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 2520 Solved Examples
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Example 1: How many factors are there for 2520?
Solution:
The factors of 2520 are too many, therefore if we can find the prime factorization of 2520, 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 2520 = 23 × 32 × 51 × 71
Therefore, the total number of factors are (3 + 1) × (2 + 1) × (1 + 1) × (1 + 1) = 4 × 3 × 2 × 2 = 48 -
Example 2: Find the Least Common Multiple and Greatest Common Factor (GCF) of 2520 and 1481.
Solution:
The factors of 2520 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 56, 60, 63, 70, 72, 84, 90, 105, 120, 126, 140, 168, 180, 210, 252, 280, 315, 360, 420, 504, 630, 840, 1260, 2520 and factors of 1481 are 1, 1481.
Therefore, the Least Common Multiple of 2520 and 1481 is 3732120 and Greatest Common Factor (GCF) of 2520 and 1481 is 1. -
Example 3: Find if 9, 12, 18, 42, 56, 63, 70 and 1134 are factors of 2520.
Solution:
When we divide 2520 by 1134 it leaves a remainder. Therefore, the number 1134 is not a factor of 2520. All numbers except 1134 are factors of 2520.
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Example 4: Find the product of all the prime factors of 2520.
Solution:
Since, the prime factors of 2520 are 2, 3, 5, 7. Therefore, the product of prime factors = 2 × 3 × 5 × 7 = 210.
FAQs on Factors of 2520
What are the Factors of 2520?
The factors of 2520 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 56, 60, 63, 70, 72, 84, 90, 105, 120, 126, 140, 168, 180, 210, 252, 280, 315, 360, 420, 504, 630, 840, 1260, 2520 and its negative factors are -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -12, -14, -15, -18, -20, -21, -24, -28, -30, -35, -36, -40, -42, -45, -56, -60, -63, -70, -72, -84, -90, -105, -120, -126, -140, -168, -180, -210, -252, -280, -315, -360, -420, -504, -630, -840, -1260, -2520.
What is the Sum of all the Factors of 2520?
Sum of all factors of 2520 = (23 + 1 - 1)/(2 - 1) × (32 + 1 - 1)/(3 - 1) × (51 + 1 - 1)/(5 - 1) × (71 + 1 - 1)/(7 - 1) = 9360
What numbers are the Pair Factors of 2520?
The pair factors of 2520 are (1, 2520), (2, 1260), (3, 840), (4, 630), (5, 504), (6, 420), (7, 360), (8, 315), (9, 280), (10, 252), (12, 210), (14, 180), (15, 168), (18, 140), (20, 126), (21, 120), (24, 105), (28, 90), (30, 84), (35, 72), (36, 70), (40, 63), (42, 60), (45, 56).
What is the Greatest Common Factor of 2520 and 2434?
The factors of 2520 and 2434 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 56, 60, 63, 70, 72, 84, 90, 105, 120, 126, 140, 168, 180, 210, 252, 280, 315, 360, 420, 504, 630, 840, 1260, 2520 and 1, 2, 1217, 2434 respectively.
Common factors of 2520 and 2434 are [1, 2].
Hence, the Greatest Common Factor (GCF) of 2520 and 2434 is 2.
How Many Factors of 2520 are also Factors of 1173?
Since, the factors of 2520 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 56, 60, 63, 70, 72, 84, 90, 105, 120, 126, 140, 168, 180, 210, 252, 280, 315, 360, 420, 504, 630, 840, 1260, 2520 and the factors of 1173 are 1, 3, 17, 23, 51, 69, 391, 1173.
Hence, [1, 3] are the common factors of 2520 and 1173.
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