Question 1. Find (GCF/HCF) of 2x2 and 12x2
Solution:
First Prime Factorize each monomial, then find common among them.
Here,
2x2 = 2 * x * x
12x2 = 2* 2 * 3 * x * x
GCF(2x2, 12x2) = 2 * x * x
= 2x2
Question 2. Find (GCF/HCF) of 6x3y and 18x2y3
Solution:
First Prime Factorize each monomial, then find common among them.
Here,
6x3y = 2 * 3 * x * x * x * y
18x2y3 = 2 * 2 * 3 * x * x * y * y * y
GCF(6x3y, 18x2y3) = 2 * 3 * x * x * y
= 6x2y
Question 3. Find (GCF/HCF) of 7x, 21x2 and 14xy2
Solution:
First Prime Factorize each monomial, then find common among them.
Here,
7x = 7 * x
21x2 = 7 * 3 * x * x
14xy2 = 7 * 2 * x * y * y
GCF(7x, 21x2, 14xy2) = 7*x
= 7x
Question 4. Find (GCF/HCF) of 42x2yz and 63x3y2z3
Solution:
First Prime Factorize each monomial, then find common among them.
Here,
42x2yz = 2 * 3 * 7 * x * x * y * z
63x3y2z3 = 3 * 3 * 7 * x * x * x * y * y * z * z * z
GCF(42x2yz, 63x3y2z3) = 3 * 7 * x * x * y * z
= 21x2yz
Question 5. Find (GCF/HCF) of 12ax2, 6a2x3 and 2a3x5
Solution:
First Prime Factorize each monomial, then find common among them.
Here,
12ax2 = 2 * 2 * 3 * a * x * x
6a2x3 = 2 * 3 * a * a * x * x * x
2a3x5 = 2 * a * a * a * x * x * x * x * x
GCF(12ax2, 6a2x3,2a3x5) = 2 * a * x * x
= 2ax2
Question 6. Find (GCF/HCF) of 9x2, 15x2y3, 6xy2 and 21x2y2
Solution:
First Prime Factorize each monomial, then find common among them.
Here,
9x2 = 3 * 3 * x * x
15x2y3 = 3 * 5 * x * x * y * y * y
6xy2 = 2 * 3 * x * y * y
21x2y2 = 3 * 7 * x * x * y * y
GCF(9x2, 15x2y3, 6xy2 and 21x2y2) = 3 * x
= 3x
Question 7. Find (GCF/HCF) of 4a2b3, -12a3b, 18a4b3
Solution:
First Prime Factorize each monomial, then find common among them.
Here,
4a2b3 = 2 * 2 * a * a * b * b * b
-12a3b = -1 * 2 * a * a * a * b
18a4b3 = 2 * 3 * 3 * a * a * a * a * b * b * b
GCF(4a2b3, -12a3b, 18a4b3) = 2 * a * a * b
= 2a2b
Question 8. Find (GCF/HCF) of 6x2y2, 9xy3, 3x3y2
Solution:
First Prime Factorize each monomial, then find common among them.
Here,
6x2y2 = 2 * 3 * x * x * y * y
9xy3 = 3 * x * y * y * y
3x3y2 = 3 * x * x * x * y * y
GCF(6x2y2, 9xy3, 3x3y2) = 3 * x * y * y
= 3xy2
Question 9. Find (GCF/HCF) of a2b3, a3b2
Solution:
First Prime Factorize each monomial, then find common among them.
Here,
a2b3 = a * a * b * b * b
a3b2 = a * a * a * b * b
GCF(a2b3, a3b2) = a * a * b * b
= a2b2
Question 10. Find (GCF/HCF) of 36a2b2c4, 54a5c2, 90a4b2c2
Solution:
First Prime Factorize each monomial, then find common among them.
Here,
36a2b2c4 = 2 * 2 * 3 * 3 * a * a * b * b * c * c * c * c
54a5c2 = 2 * 3 * 3 * 3 * a * a * a * a * a * c * c
90a4b2c2 = 2 * 3 * 3 * 5 * a * a * a * a * b * b * c * c
GCF(36a2b2c4, 54a5c2, 90a4b2c2) = 2 * 3 * 3 * a * a * c * c
= 18a2c2
Question 11. Find (GCF/HCF) of x3, -yx2
Solution:
First Prime Factorize each monomial, then find common among them.
Here,
x3 = x * x * x
-yx2 = -1 * y * x * x
GCF(x3, -yx2) = x * x
= x2
Question 12. Find (GCF/HCF) of 15a3, -45a2, -150a
Solution:
First Prime Factorize each monomial, then find common among them.
Here,
15a3 = 3 * 5 * a * a * a
-45a2 = -1 * 3 * 3 * 5 * a *a
-150a = -1 * 2 * 3 * 5 * 5 * a
GCF(15a3, -45a2, -150a) = 3 * 5 * a
= 15a
Question 13. Find (GCF/HCF) of 2x3y2, 10x2y3, 14xy
Solution:
First Prime Factorize each monomial, then find common among them.
Here,
2x3y2 = 2 * x * x * x * y * y
10x2y3 = 2 * 5 * x * x * y * y * y
14xy = 2 * 7 * x * y
GCF(2x3y2, 10x2y3, 14xy) = 2 * x * y
= 2xy
Question 14. Find (GCF/HCF) of 14x3y5, 10x5y3, 2x2y2
Solution:
First Prime Factorize each monomial, then find common among them.
Here,
14x3y5 = 2 * 7 * x * x * x * y * y * y * y * y
10x5y3 = 2 * 5 * x * x * x * x * x * y * y * y
2x2y2 = 2 * x * x * y * y
GCF(14x3y5, 10x5y3, 2x2y2) = 2 * x * x * y * y
= 2x2y2
Find the greatest common factor(GCF) of the terms in the following expressions. (Q15 – Q17)
Question 15. 5a4 + 10a3 – 15a2
Solution:
Here, 5a4 = 5 * a * a * a * a
10a3 = 2 * 5 * a * a * a
-15a2 = -1 * 3 * 5 * a * a
5a4 + 10a3 – 15a2 = (5 * a * a * a * a) + (2 * 5 * a * a * a) + (-1 * 3 * 5 * a * a)
= 5a2(a2 + 2a – 3)
GCF(5a4 + 10a3 – 15a2) = 5a2
Question 16. 2xyz + 3x2y + 4y2
Solution:
Here, 2xyz = 2 * x * y * z
3x2y = 3 * x * x * y
4y2 = 2 * 2 * y * y
2xyz + 3x2y + 4y2 = (2 * x * y * z) + (3 * x * x * y) + (4 * y * y)
= y(2x + 3x2 + 4y)
GCF(2xyz + 3x2y + 4y2) = y
Question 17. 3a2b2 + 4b2c2 + 12a2b2c2
Solution:
Here, 3a2b2 = 3 * a * a * b * b
4b2c2 = 2 * 2 * b * b * c * c
12a2b2c2 = 2 * 2 * 3 * a * a * b * b * c * c
3a2b2 + 4b2c2 + 12a2b2c2 = (3 * a * a * b * b) + (2 * 2 * b * b * c * c) + (2 * 2 * 3 * a * a * b * b * c * c)
= b(3a2b + 4bc2 + 12a2bc2)
GCF(3a2b2 + 4b2c2 + 12a2b2c2) = b
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Last Updated :
24 Nov, 2020
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