Factors of 10ab,20bc,30ca

GCF = 10

25abc

To find the factors of 10ab, 20bc, and 30ca, we can start by finding the prime factors of each term separately.

1. Factors of 10ab:
- Prime factors of 10: 2, 5
- Prime factors of ab: a, b
- Factors of 10ab: (2)(5)(a)(b) = 10ab, 5ab, 2ab, ab

2. Factors of 20bc:
- Prime factors of 20: 2, 2, 5
- Prime factors of bc: b, c
- Factors of 20bc: (2)(2)(5)(b)(c) = 20bc, 10bc, 5bc, 4bc, 2bc, bc

3. Factors of 30ca:
- Prime factors of 30: 2, 3, 5
- Prime factors of ca: c, a
- Factors of 30ca: (2)(3)(5)(c)(a) = 30ca, 15ca, 10ca, 6ca, 5ca, 3ca, 2ca, ca

Therefore, the factors of 10ab, 20bc, and 30ca are: 10ab, 5ab, 2ab, ab, 20bc, 10bc, 5bc, 4bc, 2bc, bc, 30ca, 15ca, 10ca, 6ca, 5ca, 3ca, 2ca, ca.

To find the factors of 10ab, 20bc, and 30ca, we need to break down each term into its prime factors.

The prime factors of 10ab are:
10 = 2 * 5
a = a (a is a prime factor itself)
b = b (b is a prime factor itself)

So, the factors of 10ab are:
1, 2, 5, 10, a, b, 10a, 10b, 10ab

The prime factors of 20bc are:
20 = 2 * 2 * 5
b = b (b is a prime factor itself)
c = c (c is a prime factor itself)

So, the factors of 20bc are:
1, 2, 4, 5, 10, 20, b, c, 20b, 20c, 20bc

The prime factors of 30ca are:
30 = 2 * 3 * 5
c = c (c is a prime factor itself)
a = a (a is a prime factor itself)

So, the factors of 30ca are:
1, 2, 3, 5, 6, 10, 15, 30, c, a, 30c, 30a, 30ca

Therefore, the factors of 10ab, 20bc, and 30ca are:
1, 2, 3, 4, 5, 6, 10, 15, 20, 30, a, b, c, 10a, 10b, 10ab, 20b, 20c, 20bc, 30c, 30a, 30ca.