the greatest common factor of 2x4x6x8x10 and 1x2x3x4x5 is
A. 2
B. 4
C. 8
D. 120
multiply the numbers out to find the largest product that is common to BOTH groups
Well, it seems like we have a number game going on here! Let's find out the greatest common factor of these numbers, shall we?
To find the greatest common factor, we'll look for the highest power of each common prime factor in both numbers. So, let's break it down!
For 2x4x6x8x10, let's write it as (2^1 x 2^2 x 3^1 x 2^3 x 5^1). And for 1x2x3x4x5, we can write it as (2^1 x 3^1 x 2^2 x 5^1).
To find the greatest common factor, we'll look for the lowest power of each common prime factor in both numbers. So, let's compare:
- For the 2s, the lowest power is 2^1 in both numbers.
- For the 3s, the lowest power is 3^1 in both numbers.
- For the 5s, the lowest power is 5^1 in both numbers.
Now, let's multiply these lowest powers: 2^1 x 3^1 x 5^1 = 2 x 3 x 5 = 30.
So, the greatest common factor of 2x4x6x8x10 and 1x2x3x4x5 is 30.
But hey, wait! None of the options you provided match our answer! So, I'm afraid none of the options A, B, C, or D are correct.
Math can be quite tricky sometimes! But remember, it's always important to double-check your work. Keep up the good work!
To find the greatest common factor (GCF) of two expressions, we can find the prime factorization of each expression and take the product of the common prime factors with the smallest exponent.
Prime factorization of 2x4x6x8x10:
2x4x6x8x10 = 2^1 x 2^2 x 2 x 3 x 2^3 x 5
= 2^(1+2+1+3) x 3^1 x 5
= 2^7 x 3^1 x 5
Prime factorization of 1x2x3x4x5:
1x2x3x4x5 = 2^3 x 3^1 x 5^1
Now, let's find the common prime factors with the smallest exponent:
Common factors: 2^3 x 3^1 x 5^1 = 8 x 3 x 5 = 120
Therefore, the greatest common factor (GCF) of 2x4x6x8x10 and 1x2x3x4x5 is 120.
Answer: D. 120
To find the greatest common factor (GCF) of two numbers, we need to find the largest number that divides each of the given numbers evenly.
Step 1: Write the prime factors of the two numbers.
For the first number, 2x4x6x8x10, we can break it down into its prime factors as:
2x2x2x2 x 2x2 x 3 x 2x2x2 x 5
For the second number, 1x2x3x4x5, the prime factors are simply:
2 x 3 x 2x2 x 5
Step 2: Identify the common prime factors.
Looking at the prime factorization of both numbers, we can see that the common prime factors are 2, 3, and 5.
Step 3: Multiply the common prime factors.
To find the GCF, we multiply the common prime factors: 2 x 2 x 3 x 5. This equals 60.
Therefore, the greatest common factor of 2x4x6x8x10 and 1x2x3x4x5 is 60.
Answer D. 120 is not correct, as 120 is not a factor of both numbers given.