the prime factorization of each number
18
120
56
390
144
153
GFC of each pair of numbers
16 and 20
15 and 28
33 and 66
78 and 30
9 and 36
35 and 42
100 and 120
84 and 42
GFC of each pair of monomials
15x^4 and 35x^2
-6t^3 and 9t
12ab and 12
-m^8 n^4 and 3m^6 n
12p^2 and 30q^5
27y^3 z and 45x^2 y
-8d^3 and 14d^4
10gh^2 and 5h
Prime factorization of each number:
18 = 2 * 3^2
120 = 2^3 * 3 * 5
56 = 2^3 * 7
390 = 2 * 3 * 5 * 13
144 = 2^4 * 3^2
153 = 3 * 17
GFC of each pair of numbers:
16 and 20 --> GCF = 4
15 and 28 --> GCF = 1
33 and 66 --> GCF = 33
78 and 30 --> GCF = 6
9 and 36 --> GCF = 9
35 and 42 --> GCF = 7
100 and 120 --> GCF = 20
84 and 42 --> GCF = 6
GFC of each pair of monomials:
15x^4 and 35x^2 --> GCF = 5x^2
-6t^3 and 9t --> GCF = 3t
12ab and 12 --> GCF = 12
-m^8 n^4 and 3m^6 n --> GCF = m^6
12p^2 and 30q^5 --> GCF = 2
27y^3 z and 45x^2 y --> GCF = 9y
-8d^3 and 14d^4 --> GCF = 2d^3
10gh^2 and 5h --> GCF = 5h
Skye is decorating her bedroom walls with photos. she has 36 photos of her family and 28 photos of her friends. she wants to rearrange the photos in rows so that each row has the same number of photos. so, photos of family and photos of friends do not appear in the same row.
1) how many rows will there be if Skye puts the greatest possible number of photos in each row.
2)how many photos will be in each row.
1) To find the greatest possible number of photos in each row, we need to find the greatest common factor (GCF) of 36 and 28.
The prime factorization of 36 is 2^2 * 3^2 and the prime factorization of 28 is 2^2 * 7.
The GCF of 36 and 28 is 2^2 = 4.
This means that Skye can put 4 photos in each row.
2) To find the number of rows, we divide the total number of photos of each type by the number of photos in each row:
- For family photos: 36 / 4 = 9 rows
- For friend photos: 28 / 4 = 7 rows
So, Skye will have 9 rows of family photos and 7 rows of friend photos. Each row will have 4 photos.