Math Is Fun Forum

Debbie24

Guest

math

Find two factors of 28 with a sum of 11. and Find the greatest common factor for the following numbers:  36, 72, 144.

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: math

proper factors of 28: 14,7,2,4;  7+4 = 11

for second question, this is made very easy by the fact that 36 divides both 72 and 144, since it divides both numbers, and is the smallest number, it is the greatest common factor

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ZHero

Real Member

Registered: 2008-06-08

Posts: 1,889

Re: math

Let a & b be the required factors..
So we must have..
ab = 28    ...(1)
a + b = 11 ...(2)
squaring (2) we get..
a^2 + b^2 + 2ab = 121
a^2 + b^2 = 121 - 2ab
put ab from (1) to get..
a^2 + b^2 = 121 - 2*28 = 65
now subtract 2ab from both sides to get..
a^2 + b^2 - 2ab = 65 - 2ab
(a - b)^2 = 65 - 56 = 9
-->    a - b = 3   ...(3)
now add (2) & (3)..
(a + b) + (a - b)= 11 + 3
2a = 14
a = 7
putting this a in (2)..
b = 11 - 7
b = 4
hence, required factors are 7 & 4 !!
:-)

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JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: math

ab = 28    ...(1)
a + b = 11 ...(2)

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: math

Not that it matters this time, but a and b didn't have to multiply to give 28. You could also find two factors that added to 15, for example.

I like ZHero's method for solving the simultaneous equations though!
Perhaps not the quickest way, but it's very nice.

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bilat

Member

Registered: 2008-04-23

Posts: 4

Re: math

The factor of 28:

7+ 4 =11

the greatest common factor for the following numbers:  36, 72, 144

36