Factoring and Multiples

Well, isn't that a happy little math problem we have here. To find the greatest common factor of 180, 270, and 900, we first need to find the factors of each number. Then, we look for the largest number that divides evenly into all three numbers. Let's paint a picture of this together, finding the common factors like a beautiful landscape coming together on our canvas.

It is: 70

The greatest common factor of 36 and 9 is 9. Therefore, we can factor out a 9 from the expression 36x + 9 to simplify it. This gives us 9(4x + 1) as the expression in terms of the greatest common factor.

Oh, dude, multiples are like friends at a party, they just keep showing up. So, between 49 and 95, the multiples of 2 are 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94. The multiples of 8 are 56, 64, 72, 80, 88. And the multiples of 16 are 64, 80. Hope you're not too overwhelmed by all these party guests!

5a + 5b = 5(a + b)

To find the smallest number that has 1, 2, 3, 4 and 5 as factors, you're looking for the least common multiple, or LCM, of those numbers. You can find that by listing the multiples of each number but it's faster to combine their prime factors. You need two twos, a three and a five.

2 x 2 x 3 x 5 = 60

Sure thing, honey. To find the factor tree of 275, you start by dividing it by the smallest prime number, which is 5. You get 5 x 55. Then you keep breaking down 55 until you hit prime numbers. So, the factor tree of 275 is 5 x 5 x 11. Voilà!

1: 1

2: 1, 2

3: 1, 3

4: 1, 2, 4

5: 1, 5

6: 1, 2, 3, 6

7: 1, 7

8: 1, 2, 4, 8

9: 1, 3, 9

10: 1, 2, 5, 10

11: 1, 11

12: 1, 2, 3, 4, 6, 12

13: 1, 13

14: 1, 2, 7, 14

15: 1, 3, 5, 15

16: 1, 2, 4, 8, 16

17: 1, 17

18: 1, 2, 3, 6, 9, 18

19: 1, 19

20: 1, 2, 4, 5, 10, 20

21: 1, 3, 7, 21

22: 1, 2, 11, 22

23: 1, 23

24: 1, 2, 3, 4, 6, 8, 12, 24

25: 1, 5, 25

26: 1, 2, 13, 26

27: 1, 3, 9, 27

28: 1, 2, 4, 7, 14, 28

29: 1, 29

30: 1, 2, 3, 5, 6, 10, 15, 30

31: 1, 31

32: 1, 2, 4, 8, 16, 32

33: 1, 3, 11, 33

34: 1, 2, 17, 34

35: 1, 5, 7, 35

36: 1, 2, 3, 4, 6, 9, 12, 18, 36

37: 1, 37

38: 1, 2, 19, 38

39: 1, 3, 13, 39

40: 1, 2, 4, 5, 8, 10, 20, 40

41: 1, 41

42: 1, 2, 3, 6, 7, 14, 21, 42

43: 1, 43

44: 1, 2, 4, 11, 22, 44

45: 1, 3, 5, 9, 15, 45

46: 1, 2, 23, 46

47: 1, 47

48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

49: 1, 7, 49

50: 1, 2, 5, 10, 25, 50

51: 1, 3, 17, 51

52: 1, 2, 4, 13, 26, 52

53: 1, 53

54: 1, 2, 3, 6, 9, 18, 27, 54

55: 1, 5, 11, 55

56: 1, 2, 4, 7, 8, 14, 28, 56

57: 1, 3, 19, 57

58: 1, 2, 29, 58

59: 1, 59

60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

61: 1, 61

62: 1, 2, 31, 62

63: 1, 3, 7, 9, 21, 63

64: 1, 2, 4, 8, 16, 32, 64

65: 1, 5, 13, 65

66: 1, 2, 3, 6, 11, 22, 33, 66

67: 1, 67

68: 1, 2, 4, 17, 34, 68

69: 1, 3, 23, 69

70: 1, 2, 5, 7, 10, 14, 35, 70

71: 1, 71

72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

73: 1, 73

74: 1, 2, 37, 74

75: 1, 3, 5, 15, 25, 75

76: 1, 2, 4, 19, 38, 76

77: 1, 7, 11, 77

78: 1, 2, 3, 6, 13, 26, 39, 78

79: 1, 79

80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

81: 1, 3, 9, 27, 81

82: 1, 2, 41, 82

83: 1, 83

84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

85: 1, 5, 17, 85

86: 1, 2, 43, 86

87: 1, 3, 29, 87

88: 1, 2, 4, 8, 11, 22, 44, 88

89: 1, 89

90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

91: 1, 7, 13, 91

92: 1, 2, 4, 23, 46, 92

93: 1, 3, 31, 93

94: 1, 2, 47, 94

95: 1, 5, 19, 95

96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

97: 1, 97

98: 1, 2, 7, 14, 49, 98

99: 1, 3, 9, 11, 33, 99

100: 1, 2, 4, 5, 10, 20, 25, 50, 100

5 The nearest whole number is 5. When rounding to the nearest whole number, if the number following the decimal point is less than 5, the whole number remains the same, If the number following the decimal point is greater than 5, the nearest whole number is the next whole number.

The greatest common factor or the highest common factor is the highest number that divides exactly into two or more numbers.

52: 1, 2, 4, 13, 26, 51

156: 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156

169: 1, 13, 169

The GCF of 52, 156 and 169 is 13.

The greatest common factor (GCF) is often also called the greatest common divisor (GCD) or highest common factor (HCF). Keep in mind that these different terms all refer to the same thing: the largest integer which evenly divides two or more numbers.

The greatest common factor of 384 and 512 is 128

Half of 12.3 is 6.15. To find half of a number, you simply divide it by 2. In this case, 12.3 divided by 2 equals 6.15.

Oh, what a happy little question! Let's paint a picture of the multiples of 7 up to 126. We start with 7, then add 7 to get 14, then 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, and finally 126. Just like painting, math can be a beautiful and calming experience.

Well, honey, the common factors of eighty-eight are 1, 2, 4, 8, 11, 22, 44, and 88. So, if you're looking to divide eighty-eight into nice, even chunks, those are the numbers you'll wanna play with. Just remember, math doesn't have to be boring - embrace those factors like the sassy diva you are!

The factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.
The prime factors of 72 are: 2 and 3.

The factors of 96 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.
The prime factors of 96 are: 2 and 3.

The first 100 multiples of 7:

7, 14, 21, 28, 35, 42, 49, 56, 63, 70,

77, 84, 91, 98, 105, 112, 119, 126, 133, 140,

147, 154, 161, 168, 175, 182, 189, 196, 203, 210,

217, 224, 231, 238, 245, 252, 259, 266, 273, 280,

287, 294, 301, 308, 315, 322, 329, 336, 343, 350,

357, 364, 371, 378, 385, 392, 399, 406, 413, 420,

427, 434, 441, 448, 455, 462, 469, 476, 483, 490,

497, 504, 511, 518, 525, 532, 539, 546, 553, 560,

567, 574, 581, 588, 595, 602, 609, 616, 623, 630,

637, 644, 651, 658, 665, 672, 679, 686, 693, 700

Oh, absolutely! It sounds like you're looking for a number that can divide both 32 and 47. In this case, the number 1 can divide both of these numbers evenly, as can the number itself. Remember, there's always a way to find common ground and make things work out beautifully.

Oh, what a happy little math problem we have here! To find the greatest common factor of 217, 93, and 155, we can start by finding the factors of each number. Then, we look for the largest number that is a factor of all three - that's our greatest common factor! Just like painting a beautiful landscape, with a little patience and attention to detail, we can find the answer together.

Oh, dude, the highest common factor of 40 and 120 is 40. Like, you take the largest number that can divide both 40 and 120 evenly, and that's it. It's like finding the biggest slice of pizza that can be shared between two hungry friends.

The prime factorization of 1800 can be found by breaking it down into its prime factors: 2 x 2 x 2 x 3 x 3 x 5 x 5. This can be written in exponential form as 2^3 x 3^2 x 5^2. This means that 1800 can be expressed as the product of these prime numbers raised to their respective exponents.

Well, darling, the highest common factor of 210 and 108 is 6. That's right, just good old number 6 strutting its stuff as the biggest factor those two can share. So, there you have it, 6 is the boss in this math equation.

It is the same principle as coins and notes. You can easily make up any [whole] number using a selection of these values.

The most efficient set would be powers of 2 but most people would not want to calculate 77, for example, from powers of 2. It is 64 + 8 + 4 + 1. In terms of the selection you have, it is 50 + 20 + 5 + 2. Same number of resistors but easier to add up (maybe!).

Oh, what a happy little question! The first five multiples of 18 are 18, 36, 54, 72, and 90. Just imagine each multiple as a little tree in a row, swaying gently in the breeze. Keep painting those multiples, and soon you'll have a whole forest of numbers to admire!