Answer:
Explanation:
Since
16
x
5
y
2
,
40
x
4
y
3
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
16
x
5
y
2
,
40
x
4
y
3
:
1. Find the GCF for the numerical part
16
,
40
2. Find the GCF for the variable part
x
5
,
y
2
,
x
4
,
y
3
3. Multiply the values together
Find the common factors for the numerical part:
16
,
40
The factors for
16
are
1
,
2
,
4
,
8
,
16
.
Tap for more steps...
1
,
2
,
4
,
8
,
16
The factors for
40
are
1
,
2
,
4
,
5
,
8
,
10
,
20
,
40
.
Tap for more steps...
1
,
2
,
4
,
5
,
8
,
10
,
20
,
40
List all the factors for
16
,
40
to find the common factors.
16
:
1
,
2
,
4
,
8
,
16
40
:
1
,
2
,
4
,
5
,
8
,
10
,
20
,
40
The common factors for
16
,
40
are
1
,
2
,
4
,
8
.
1
,
2
,
4
,
8
The GCF for the numerical part is
8
.
GCF
Numerical
=
8
Next, find the common factors for the variable part:
x
5
,
y
2
,
x
4
,
y
3
The factors for
x
5
are
x
⋅
x
⋅
x
⋅
x
⋅
x
.
x
⋅
x
⋅
x
⋅
x
⋅
x
The factors for
y
2
are
y
⋅
y
.
y
⋅
y
The factors for
x
4
are
x
⋅
x
⋅
x
⋅
x
.
x
⋅
x
⋅
x
⋅
x
The factors for
y
3
are
y
⋅
y
⋅
y
.
y
⋅
y
⋅
y
List all the factors for
x
5
,
y
2
,
x
4
,
y
3
to find the common factors.
x
5
=
x
⋅
x
⋅
x
⋅
x
⋅
x
y
2
=
y
⋅
y
x
4
=
x
⋅
x
⋅
x
⋅
x
y
3
=
y
⋅
y
⋅
y
The common factors for the variables
x
5
,
y
2
,
x
4
,
y
3
are
x
⋅
x
⋅
x
⋅
x
⋅
y
⋅
y
.
x
⋅
x
⋅
x
⋅
x
⋅
y
⋅
y
The GCF for the variable part is
x
4
y
2
.
GCF
Variable
=
x
4
y
2
Multiply the GCF of the numerical part
8
and the GCF of the variable part
x
4
y
2
.
8
x
4
y
2