Factoring and Multiples

163.86

2^(4) x 3^(1) =48 in exponential form

Mean is the sum(addition) of all the terms , divided by the number of terms.

Median is the absolute middle term, when placed in rank order.

Mode is the most frequently occurring term.

15 27 10 25 9 22 25

First place these terms in rank order. Ther are seven(7) terms.

9,10,15,22,25,25,27.

MEAN => (9+10+15+22+25+25+27) / 7 = 133/7 = 19

Median = 22 ( The absolute middle term.

Mode = 25 (The most frequent ; because it occurs twice, whereas the rest are only once).

1, 3, and 9 are the common factors.

lcm(11,18)

Factor the expressions that are not already factored.

18=2 x 3²

Identify all the factors and their highest power in all expressions. Multiply the highest powers of these factors to get the least common multiple.

2 x 3² x 11

Expand the expression.

198

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504.

2 x 2 x 2 x 3 x 3 x 5

The factors of 105 are 3,5, & 7.

The factors of 63 are 3,3, & 7.

One lot of '3' and one lot of '7' is common to both numbers.

Hence 3 x 7 = 21 , which is the HCF of 105,& 63.

Factors of 18 are 3,3,& 2.

Factors of 21 are 3 & 7

One lot of '3' is common to both so '3' is the HCF.

Greatest common factor for 52 and 91 is 13.

The greatest common factor of 33 and 69 is 3

Any numerical value ending in zero (0) is divisioble by 10.

10,20,30,40,50,60,70,80,90,100, 1000, 1,000,000, 1,000,000,000 are all divisible by '10'.

NB THere millions more numbers divisible by '10' , provided they and with a zero(0).

Taking a fraction like '50'/100'. This can be reduced to '1/2'.

How do we do it?

We notice that both '50' and '100' are even number ; end in '0' so they will divide by '2'

So divide top and bottom by '2'

50/100 = 25/50. We now notice that both '25' and '50' end in '5' or '0', so they will divide by '5'

So divide top and bottom by '5'

25/50 = 5/10

We now notice again, that both '5' and '10' end in '5' or '0', so they will divide by '5'

So divide top and bottom by '5'

Hence 5/10 = 1/2

So overall 50/100 = 1/2

NB An appreciation of the multiplication tables is required.

NNB Dividing top and bottom is sometimes referred to as 'cancelling down'.

50

10 and -9

common factor in -36 and 63

10.01, 10.10, 101.1

NO!!! '7' is a FACTOR of '42'.

However, '42' is a multiple of '7'.

Since 36 is a factor of 72, all of its factors are included in the factors of 72.

The GCF is 8.

1, 2, 4.

4

7 factorial means 7x6x5x4x3x2x1

which can be rewritten as 7x(3x2)x5x(2x2)x3x2x1 when 6 and 4 are factored.

Notice the repeating factors are (3x3)x(2x2)x(2x2) = (3x2x2)x(3x2x2) = 12 squared = 144

33 x 72 = 1323

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