find the common factors of the given terms.
1)12x,36
2)2y,22xy
Answers
Step-by-step explanation:
12x, 36
(ii) 2y, 22xy
(iii) 14\ pq,\ 28p^2q^214 pq, 28p
2
q
2
(iv) 2x,3x^2,\ 42x,3x
2
, 4
(v) 6abc,\ 24ab^2,\ 12a^2b6abc, 24ab
2
, 12a
2
b
(vi) 16x^3,\ -4x^2,\ 32x16x
3
, −4x
2
, 32x
(vii) 10\ pq,\ 20qr,\ 30rp10 pq, 20qr, 30rp
(viii) 3x^2y^3,\ 10x^3y^2,\ 6x^2y^2z3x
2
y
3
, 10x
3
y
2
, 6x
2
y
2
z
Solution 1:
(i) 12x\ =\ 12\times x12x = 12×x
36\ =\ 12\times336 = 12×3
common factor = 12
(ii) 2y=2\times y2y=2×y
22xy=\ 2\times11\times x\times y22xy= 2×11×x×y
common factor = 2,y
(iii) 14\ pq\ =\ p\times q\times7\times214 pq = p×q×7×2
28p^2q^2\ =\ 2\times2\times7\times p\times p\times q\times q28p
2
q
2
= 2×2×7×p×p×q×q
Common factor =7\times2\times p\times q\ =14pq7×2×p×q =14pq
(iv) 2x=\ 2\times x\times12x= 2×x×1
3\times x\times x\times13×x×x×1
4=\ 2\times2\times14= 2×2×1
common factor =1
(v) 6abc\ =\ 2\times3\times a\times b\times c6abc = 2×3×a×b×c
24\ ab^2\ =\ 2\times3\times4\times a\times b\times b24 ab
2
= 2×3×4×a×b×b
12a^2b\ =2\times2\times3\times a\times a\times b12a
2
b =2×2×3×a×a×b
Common factor = 2\times3\times a\times b\ =\ 6ab2×3×a×b = 6ab
(vi) 16x^{3\ }=\ 2\times2\times2\times2\times x\times x\times x16x
3
= 2×2×2×2×x×x×x
-4x^2=\ 2\times2\times x\times x\times\left(-1\right)−4x
2
= 2×2×x×x×(−1)
32x\ =\ 2\times2\times2\times2\times2\times2\times x32x = 2×2×2×2×2×2×x
common factor = 2\times2\times x\ =4x2×2×x =4x
(vii) 10pq=2\times5\times p\times q10pq=2×5×p×q
20qr\ =\ 2\times2\times5\times q\times r20qr = 2×2×5×q×r
30rp\ =\ 3\times2\times5\times r\times p30rp = 3×2×5×r×p
common factor = 2\times5=102×5=10
(viii) 3x^2y^2=\ 3\times x\times x\times y\times y\times y3x
2
y
2
= 3×x×x×y×y×y
10x^3y^2=\ 2\times5\times x\times x\times x\times y\times y10x
3
y
2
= 2×5×x×x×x×y×y
6x^2y^2z\ =\ 2\times3\times x\times x\times y\times y\times z6x
2
y
2
z = 2×3×x×x×y×y×z
common factor = x^2y^2x
2
y
2
Answer:
1)12x,36 = 12
2)2y,22xy = 2y