Help on question?

Question

Can someone tell me the GCF's of these problems? :o
1)14,21
2)25,100
3) 57, 84
4)54,144
5)8,16,20
6)12,15,21
7)90,900
8)143,169
9)z,z(to the power of two)
10)5a,35a
11)19c(to the power of 3),24c(to the power of 3)
12)180a(power of two),210a
13)48r(power of two)s,63s
14)6m(power of three)n,8mn(poewr of two)
15)27x(poer of two)y(power of three), 46x(power of two)y
16)25b(power of two)x, 42bc

Answer 1

Okay, rather than just give you the answers, let me explain how to do these problems. GCF (also known as GCD) stands for Greatest Common Factor (or Greatest Common Divisor). So, you are looking for the largest possible number that divides all elements, i.e. gcd(a,b,...,k) = d and gcd(a/d, b/d, ..., k/d) = 1.

So, let's pick a couple to get an idea.

1. 14, 21. What I do is I write down each number in it's prime factorization. Then, I pick out the highest exponent of each prime that the elements share. 14 = 7 * 2, 21 = 7 * 3. So, the GCF of 14 and 21 is 7.

8. 143, 169. 143 = 11 * 13, 169 = 13 * 13 = 13^2. Both 143 and 169 share the factor 13, and the largest exponent they both share would be 13^1, so GCF(143, 169) = 13.

The remaining questions involve variables, but these are solved in the same manner.

10. 5a, 35a. 5a = 5 * a, 35a = 7 * 5 * a. So, the GCF (5a, 35a) = 5a.

15. 27 x^2 y^3, 46 x^2 y. 27x^2 y^3 = 3^3*x^2*y^3, and 46 x^2 y = 23 * 2 * x^2 * y. So, these two elements have factors in common of x^2 and y. Notice, both terms have y included, but the largest exponent of y that both terms have in common is y^1. So, gcf(27x^2 y^3, 46x^2 y) = x^2 y.

I hope this helps, and I think you should be able to finish the rest of your homework assignment given these methods.

Answer 2

1. 7
2. 25
3. 3
4. 8
5. 4
6. 3
7. 90
8.
9. z
10. 5a
11. c^3

Answer 3

8) 13
12) 30a
13) 3s
14) 2mn
15) x^2y
16) b

Answer 4

sorry. what's GCF?