Factors of 5040 in pair are (1, 5040) , (2, 2520) , (3, 1680) , (4, 1260) , (5, 1008) , (6, 840) , (7, 720) , (8, 630) , (9, 560) , (10, 504) , (12, 420) , (14, 360) , (15, 336) , (16, 315) , (18, 280) , (20, 252) , (21, 240) , (24, 210) , (28, 180) , (30, 168) , (35, 144) , (36, 140) , (40, 126) , (42, 120) , (45, 112) , (48, 105) , (56, 90) , (60, 84) , (63, 80) and (70, 72)
| Factor Pair | Pair Factorization |
|---|---|
| 1 and 5040 | 1 x 5040 = 5040 |
| 2 and 2520 | 2 x 2520 = 5040 |
| 3 and 1680 | 3 x 1680 = 5040 |
| 4 and 1260 | 4 x 1260 = 5040 |
| 5 and 1008 | 5 x 1008 = 5040 |
| 6 and 840 | 6 x 840 = 5040 |
| 7 and 720 | 7 x 720 = 5040 |
| 8 and 630 | 8 x 630 = 5040 |
| 9 and 560 | 9 x 560 = 5040 |
| 10 and 504 | 10 x 504 = 5040 |
| 12 and 420 | 12 x 420 = 5040 |
| 14 and 360 | 14 x 360 = 5040 |
| 15 and 336 | 15 x 336 = 5040 |
| 16 and 315 | 16 x 315 = 5040 |
| 18 and 280 | 18 x 280 = 5040 |
| 20 and 252 | 20 x 252 = 5040 |
| 21 and 240 | 21 x 240 = 5040 |
| 24 and 210 | 24 x 210 = 5040 |
| 28 and 180 | 28 x 180 = 5040 |
| 30 and 168 | 30 x 168 = 5040 |
| 35 and 144 | 35 x 144 = 5040 |
| 36 and 140 | 36 x 140 = 5040 |
| 40 and 126 | 40 x 126 = 5040 |
| 42 and 120 | 42 x 120 = 5040 |
| 45 and 112 | 45 x 112 = 5040 |
| 48 and 105 | 48 x 105 = 5040 |
| 56 and 90 | 56 x 90 = 5040 |
| 60 and 84 | 60 x 84 = 5040 |
| 63 and 80 | 63 x 80 = 5040 |
| 70 and 72 | 70 x 72 = 5040 |
Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 5040. They are called negative pair factors.
Hence, the negative pairs of 5040 would be ( -1 , -5040 ) .
In mathematics, factor pair are often given as pair of numbers which when multiplied together give the original number. Every natural number is a product of atleast one factor pair. Eg- Factors of 5040 are 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 12 , 14 , 15 , 16 , 18 , 20 , 21 , 24 , 28 , 30 , 35 , 36 , 40 , 42 , 45 , 48 , 56 , 60 , 63 , 70 , 72 , 80 , 84 , 90 , 105 , 112 , 120 , 126 , 140 , 144 , 168 , 180 , 210 , 240 , 252 , 280 , 315 , 336 , 360 , 420 , 504 , 560 , 630 , 720 , 840 , 1008 , 1260 , 1680 , 2520 , 5040. So, factors of 5040 in pair are (1,5040), (2,2520), (3,1680), (4,1260), (5,1008), (6,840), (7,720), (8,630), (9,560), (10,504), (12,420), (14,360), (15,336), (16,315), (18,280), (20,252), (21,240), (24,210), (28,180), (30,168), (35,144), (36,140), (40,126), (42,120), (45,112), (48,105), (56,90), (60,84), (63,80), (70,72).
In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.
Hence, Factors of 5040 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 48, 56, 60, 63, 70, 72, 80, 84, 90, 105, 112, 120, 126, 140, 144, 168, 180, 210, 240, 252, 280, 315, 336, 360, 420, 504, 560, 630, 720, 840, 1008, 1260, 1680, 2520, and 5040
Yes 5040 is a composite number.
No 5040 is not a prime number.
Factors of 5040 are 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 12 , 14 , 15 , 16 , 18 , 20 , 21 , 24 , 28 , 30 , 35 , 36 , 40 , 42 , 45 , 48 , 56 , 60 , 63 , 70 , 72 , 80 , 84 , 90 , 105 , 112 , 120 , 126 , 140 , 144 , 168 , 180 , 210 , 240 , 252 , 280 , 315 , 336 , 360 , 420 , 504 , 560 , 630 , 720 , 840 , 1008 , 1260 , 1680 , 2520 , 5040. therefore mean of factors of 5040 is (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 12 + 14 + 15 + 16 + 18 + 20 + 21 + 24 + 28 + 30 + 35 + 36 + 40 + 42 + 45 + 48 + 56 + 60 + 63 + 70 + 72 + 80 + 84 + 90 + 105 + 112 + 120 + 126 + 140 + 144 + 168 + 180 + 210 + 240 + 252 + 280 + 315 + 336 + 360 + 420 + 504 + 560 + 630 + 720 + 840 + 1008 + 1260 + 1680 + 2520 + 5040) / 60 = 322.40.
A number x is said to be the proper divisor of y if it divides y completely, given that x is smaller than y.
An improper divisor of a number is the number itself apart from this any divisor of a given number is a proper divisor.
Factors of 5040 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 48, 56, 60, 63, 70, 72, 80, 84, 90, 105, 112, 120, 126, 140, 144, 168, 180, 210, 240, 252, 280, 315, 336, 360, 420, 504, 560, 630, 720, 840, 1008, 1260, 1680, 2520, 5040. So, factors of 5040 in pair are (1,5040), (2,2520), (3,1680), (4,1260), (5,1008), (6,840), (7,720), (8,630), (9,560), (10,504), (12,420), (14,360), (15,336), (16,315), (18,280), (20,252), (21,240), (24,210), (28,180), (30,168), (35,144), (36,140), (40,126), (42,120), (45,112), (48,105), (56,90), (60,84), (63,80), (70,72).
Negative factors of 5040 are -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -12, -14, -15, -16, -18, -20, -21, -24, -28, -30, -35, -36, -40, -42, -45, -48, -56, -60, -63, -70, -72, -80, -84, -90, -105, -112, -120, -126, -140, -144, -168, -180, -210, -240, -252, -280, -315, -336, -360, -420, -504, -560, -630, -720, -840, -1008, -1260, -1680, -2520, -5040. Hence, factors of 5040 in pair are (-1,-5040), (-2,-2520), (-3,-1680), (-4,-1260), (-5,-1008), (-6,-840), (-7,-720), (-8,-630), (-9,-560), (-10,-504), (-12,-420), (-14,-360), (-15,-336), (-16,-315), (-18,-280), (-20,-252), (-21,-240), (-24,-210), (-28,-180), (-30,-168), (-35,-144), (-36,-140), (-40,-126), (-42,-120), (-45,-112), (-48,-105), (-56,-90), (-60,-84), (-63,-80), (-70,-72).
Factors of 5040 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 48, 56, 60, 63, 70, 72, 80, 84, 90, 105, 112, 120, 126, 140, 144, 168, 180, 210, 240, 252, 280, 315, 336, 360, 420, 504, 560, 630, 720, 840, 1008, 1260, 1680, 2520, 5040. Positive factors of 5040 in pair are (1,5040), (2,2520), (3,1680), (4,1260), (5,1008), (6,840), (7,720), (8,630), (9,560), (10,504), (12,420), (14,360), (15,336), (16,315), (18,280), (20,252), (21,240), (24,210), (28,180), (30,168), (35,144), (36,140), (40,126), (42,120), (45,112), (48,105), (56,90), (60,84), (63,80), (70,72). Negative factors of 5040 in pair are (-1,-5040), (-2,-2520), (-3,-1680), (-4,-1260), (-5,-1008), (-6,-840), (-7,-720), (-8,-630), (-9,-560), (-10,-504), (-12,-420), (-14,-360), (-15,-336), (-16,-315), (-18,-280), (-20,-252), (-21,-240), (-24,-210), (-28,-180), (-30,-168), (-35,-144), (-36,-140), (-40,-126), (-42,-120), (-45,-112), (-48,-105), (-56,-90), (-60,-84), (-63,-80), (-70,-72).
Factors of 5040 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 48, 56, 60, 63, 70, 72, 80, 84, 90, 105, 112, 120, 126, 140, 144, 168, 180, 210, 240, 252, 280, 315, 336, 360, 420, 504, 560, 630, 720, 840, 1008, 1260, 1680, 2520, 5040. So the product of all factors of 5040 would be 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 12 x 14 x 15 x 16 x 18 x 20 x 21 x 24 x 28 x 30 x 35 x 36 x 40 x 42 x 45 x 48 x 56 x 60 x 63 x 70 x 72 x 80 x 84 x 90 x 105 x 112 x 120 x 126 x 140 x 144 x 168 x 180 x 210 x 240 x 252 x 280 x 315 x 336 x 360 x 420 x 504 x 560 x 630 x 720 x 840 x 1008 x 1260 x 1680 x 2520 x 5040 = 1.182813011613388e+111.
Factors of 5040 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 48, 56, 60, 63, 70, 72, 80, 84, 90, 105, 112, 120, 126, 140, 144, 168, 180, 210, 240, 252, 280, 315, 336, 360, 420, 504, 560, 630, 720, 840, 1008, 1260, 1680, 2520, 5040. Prime factors are 2, 2, 2, 2, 3, 3, 5, 7. So, the product of all prime factors of 5040 would be 2 x 2 x 2 x 2 x 3 x 3 x 5 x 7 = 5040.
Factors of 5040 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 48, 56, 60, 63, 70, 72, 80, 84, 90, 105, 112, 120, 126, 140, 144, 168, 180, 210, 240, 252, 280, 315, 336, 360, 420, 504, 560, 630, 720, 840, 1008, 1260, 1680, 2520, 5040.Factors of 5040 in pair are (1,5040), (2,2520), (3,1680), (4,1260), (5,1008), (6,840), (7,720), (8,630), (9,560), (10,504), (12,420), (14,360), (15,336), (16,315), (18,280), (20,252), (21,240), (24,210), (28,180), (30,168), (35,144), (36,140), (40,126), (42,120), (45,112), (48,105), (56,90), (60,84), (63,80), (70,72).
To arrange 5040 blocks in all possible ways to form a rectangle, we need to calculate factors of 5040 in pair. Therefore, factors of 5040 in pair are (1,5040), (2,2520), (3,1680), (4,1260), (5,1008), (6,840), (7,720), (8,630), (9,560), (10,504), (12,420), (14,360), (15,336), (16,315), (18,280), (20,252), (21,240), (24,210), (28,180), (30,168), (35,144), (36,140), (40,126), (42,120), (45,112), (48,105), (56,90), (60,84), (63,80), (70,72)