Answer:
Step-by-step explanation:
Since
14
X
,
4
X
Y
,
−
18
X
Y
2
contain both numbers and variables, there are two steps to find the GCF (HCF). Find GCF for the numeric part then find GCF for the variable part.
Steps to find the GCF for
14
X
,
4
X
Y
,
−
18
X
Y
2
:
1. Find the GCF for the numerical part
14
,
4
,
−
18
2. Find the GCF for the variable part
X
1
,
X
1
,
Y
1
,
X
1
,
Y
2
3. Multiply the values together
Find the common factors for the numerical part:
14
,
4
,
−
18
The factors for
14
are
1
,
2
,
7
,
14
.
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1
,
2
,
7
,
14
The factors for
4
are
1
,
2
,
4
.
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The factors for
4
are all numbers between
1
and
4
, which divide
4
evenly.
Check numbers between
1
and
4
Find the factor pairs of
4
where
x
⋅
y
=
4
.
x
y
1
4
2
2
List the factors for
4
.
1
,
2
,
4
The factors for
−
18
are
−
18
,
−
9
,
−
6
,
−
3
,
−
2
,
−
1
,
1
,
2
,
3
,
6
,
9
,
18
.
Tap for fewer steps...
The factors for
−
18
are all numbers between
1
and
18
, which divide
−
18
evenly.
Check numbers between
1
and
18
Find the factor pairs of
−
18
where
x
⋅
y
=
−
18
.
List the factors for
−
18
.
−
18
,
−
9
,
−
6
,
−
3
,
−
2
,
−
1
,
1
,
2
,
3
,
6
,
9
,
18
List all the factors for
14
,
4
,
−
18
to find the common factors.
14
:
1
,
2
,
7
,
14
4
:
1
,
2
,
4
−
18
:
−
18
,
−
9
,
−
6
,
−
3
,
−
2
,
−
1
,
1
,
2
,
3
,
6
,
9
,
18
The common factors for
14
,
4
,
−
18
are
1
,
2
.
1
,
2
The GCF for the numerical part is
2
.
GCF
Numerical
=
2
Next, find the common factors for the variable part:
X
,
X
,
Y
,
X
,
Y
2
The factor for
X
1
is
X
itself.
X
The factor for
Y
1
is
Y
itself.
Y
The factor for
X
1
is
X
itself.
X
The factors for
Y
2
are
Y
⋅
Y
.
Y
⋅
Y
List all the factors for
X
1
,
X
1
,
Y
1
,
X
1
,
Y
2
to find the common factors.
X
1
=
X
X
1
=
X
Y
1
=
Y
X
1
=
X
Y
2
=
Y
⋅
Y
The common factor for the variables
X
1
,
X
1
,
Y
1
,
X
1
,
Y
2
is
X
.
X
The GCF for the variable part is
X
.
GCF
Variable
=
X
Multiply the GCF of the numerical part
2
and the GCF of the variable part
X
.
2
X
