Prime Numbers
A Prime Number can be divided evenly only by 1 or itself and it must be a whole number greater than 1.
Thus following are Prime Numbers less than 100.
Thus following are Prime Numbers less than 100.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
Composite Numbers
Other numbers have at least two factors. They are called as composite numbers.
They are as follows
4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100.
They are as follows
4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100.
Factors for all numbers from 1 to 100 (excluding 1 and the same number)
1, 2, 3, 4(2), 5, 6(2, 3), 7, 8(2, 4), 9(3, 3), 10(2, 5)
——
11, 12(2, 3, 6), 13, 14(2, 7), 15(3, 5), 16(2, 4, 8), 17, 18(2, 3, 6, 9), 19, 20(2, 4, 5, 10)
——
21(3, 7), 22(2, 11), 23, 24(2, 3, 6, 8, 12), 25(5, 5), 26(2, 13), 27(3, 9), 28(2, 4, 7, 14), 29, 30(2, 3, 5, 6, 15)
——
31, 32(2, 4, 8, 16), 33(3, 11), 34(2, 17), 35(5, 7), 36(2, 3, 4, 6, 9, 12, 18), 37, 38(2, 19), 39(3, 13), 40(2, 4, 5, 8, 10, 20),
——
41, 42(2, 3, 7, 21), 43, 44(2, 4, 11, 22), 45(3, 5, 9, 15), 46(2, 23), 47, 48(2, 3, 4, 6, 8, 12, 16, 24), 49(7, 7), 50(2, 5, 10)
——
51(3, 17), 52(2, 4, 13, 26), 53, 54(2, 3, 6, 9, 18, 27), 55(5, 11), 56(2, 4, 7, 8, 14, 28), 57(3, 19), 58(2, 29), 59, 60(2, 4, 5, 6, 10, 12, 15, 30)
——
61, 62(2, 31), 63(3, 7, 21), 64(2, 4, 8, 16, 32)
65(5, 13), 66(2, 3, 6, 11, 22, 33), 67, 68(2, 4, 17, 34), 69(3, 23), 70(2, 5, 7, 10, 14, 35)
——
71, 72(2, 3, 4, 6, 8, 9, 12, 18, 24, 36),
73, 74(2, 37), 75(3, 5, 15, 25), 76(2, 4, 19, 38), 77(7, 11), 78(2, 3, 6, 13, 26, 39), 79, 80(2, 4, 5, 8, 10, 20, 40)
——
81(3, 9, 27), 82(2, 41), 83,84(2, 3, 6, 7, 14, 28, 42), 85(5,17), 86(2, 43), 87(3, 19), 88(2, 4, 8, 11, 22, 44), 89, 90(2, 5, 6, 9, 10, 15, 18, 30, 45)
——
91(7, 13), 92(2, 23, 46), 93(3, 31), 94(2, 47), 95(5, 19), 96( 2, 3, 4, 6, 8, 12, 16, 24, 32, 48), 97, 98(2, 7, 14, 49), 99(3, 9, 11, 33), 100(2, 4, 5, 10, 20, 25, 50)
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I have listed below all factor combinations for numbers from 1 to 100 which will serve as a ready reckoner for elementary school children while solving arithmetic examples.
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I have listed below all factor combinations for numbers from 1 to 100 which will serve as a ready reckoner for elementary school children while solving arithmetic examples.
(Prime Numbers are shown in Bold font)
1, 2, 3, 4(2x2), 5, 6(2x3), 7, 8(2x4, 2x2x2), 9(3x3), 10(2x5)
——
11, 12(2x6, 2x2x3), 13, 14(2x7), 15(3x5), 16(2x8, 2x2x4, 2x2x2x2), 17, 18(2x9, 2x3x3, 6x3), 19, 20(2x10, 2x2x5, 4x5)
——
21(3x7), 22(2x11), 23, 24(2x12, 2x2x6, 2x2x2x3, 8x3), 25(5x5), 26(2x13), 27(3x9, 3x3x3), 28(2x14, 2x2x7), 29, 30(2x15, 2x3x5, 6x5)
——
31, 32(2x16, 2x2x8, 2x2x2x4, 2x2x2x2x2), 33(3x11), 34(2x17), 35(5x7), 36(2x18, 2x2x9, 6x6, 2x3x6, 3x3x4, 2x2x3x3, 3x12), 37, 38(2x19), 39(3x13), 40(2x20, 2x2x10, 2x2x2x2x5, 2x4x5, 8x5),
——
41, 42(2x21, 2x3x7), 43, 44(2x22, 2x2x11, 4x11), 45(3x15, 3x3x5, 5x9), 46(2x23), 47, 48(2x24, 2x2x12, 2x2x2x6, 2x2x2x2x3, 2x8x3), 49(7x7), 50(2x5x5, 5x10)
——
51(3x17), 52(2x26, 2x2x13), 53, 54(2x27, 2x3x9, 2x3x3x3,6x9), 55(5x11), 56(2x28, 2x2x14, 4x14, 7x8), 57(3x19), 58(2x29), 59, 60(2x30, 2x2x15, 2x2x3x5, 2x6x5)
——
61, 62(2x31), 63(3x21, 3x3,7), 64(2x32, 2x2x16, 2x2x2x8, 2x2x2x2x4, 2x2x2x2x2x2)
65(5x13), 66(2x33, 2x3x11, 6x11), 67, 68(2x34, 2x2x17, 4x17), 69(3x23), 70(2x35, 2x5x7, 10x7)
——
71, 72(2x36, 2x2x18, 2x2x2x9, 2x6x6, 2x2x3x6, 2x3x3x4, 2x2x2x3x3, 3x12),
73, 74(2x37), 75(3x25, 5x15), 76(2x38, 2x2x19, 4x19), 77(7x11), 78(2x39, 2x3x13, 6x13), 79, 80(2x40, 2x2x20, 2x2x2x10, 2x2x2x2x2x5, 2x2x4x5, 2x8x5)
——
81(3x27, 9x9), 82(2x41), 83,84(2x42, 2x2x21, 6x14),85(5x17), 86(2x43), 87(3x19), 88(2x44, 2x2x22, 2x2x2x11, 2x4x11), 89, 90(2x45, 3x30, 2x5x9, 6x15, 9x10)
——
91(7x13), 92(2x46, 4x23), 93(3x31), 94(2x47), 95(5x19), 96( 2x2x24, 2x2x2x12, 2x2x2x2x6, 2x2x2x2x2x3, 2x2x8x3, 3x32, 6x16, 12x8, 24x4, 48x2), 97, 98(2x49, 14x7), 99(3x33, 9x11), 100(2x50, 2x2x25, 5x20, 10x10)
———
It is seen that numbers who have only one factor set with 2 numbers are 34 as given below
4, 6, 9, 10, 14, 15, 21, 22, 25, 26, 33, 34, 35, 38, 39, 46, 49, 51, 55, 57, 58, 62, 65, 69, 74, 77, 82, 85, 86, 87, 91, 93, 94, 95
Moreover, 1 and other prime numbers who do not have factors (other than 1) are 26
Thus 34+26=60 numbers need to be memorised.
Other factors can be easily derived from these numbers. Out of that also if we if we strike out multipliers of 2 from remaining numbers, we have to concentrate only on 8 numbers for multiple factor sets.
The factor sets for some few numbers are worth remembering
80 has 6 factor sets, 36 has 7 factor sets, 72 has 8 factor sets and 96 has total 10 factor sets.
It is seen that numbers who have only one factor set with 2 numbers are 34 as given below
4, 6, 9, 10, 14, 15, 21, 22, 25, 26, 33, 34, 35, 38, 39, 46, 49, 51, 55, 57, 58, 62, 65, 69, 74, 77, 82, 85, 86, 87, 91, 93, 94, 95
Moreover, 1 and other prime numbers who do not have factors (other than 1) are 26
Thus 34+26=60 numbers need to be memorised.
Other factors can be easily derived from these numbers. Out of that also if we if we strike out multipliers of 2 from remaining numbers, we have to concentrate only on 8 numbers for multiple factor sets.
The factor sets for some few numbers are worth remembering
80 has 6 factor sets, 36 has 7 factor sets, 72 has 8 factor sets and 96 has total 10 factor sets.
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