adding and subtraction number using greatest common factors 940-420=? 169-26=? 15+75-45=? 48+16=? 17+51=? What is the GCF?
To add and subtract numbers using the greatest common factors (GCF), you need to follow these steps:
Step 1: Determine the GCF of the given numbers.
Step 2: Use the GCF to simplify the numbers to their lowest terms.
Step 3: Perform the addition or subtraction operation using the simplified numbers.
Step 4: If necessary, express the resulting answer in its simplest form.
Now, let's solve the given problems one by one:
1. 940 - 420:
Step 1: Find the GCF of 940 and 420.
The prime factorization of 940: 2 * 2 * 5 * 47
The prime factorization of 420: 2 * 2 * 3 * 5 * 7
The common factors are 2, 2, and 5.
So, the GCF of 940 and 420 is 2 * 2 * 5 = 20.
Step 2: Simplify the numbers.
940 can be simplified as 20 * 47.
420 can be simplified as 20 * 3 * 7.
Step 3: Perform the subtraction.
(20 * 47) - (20 * 3 * 7) = 940 - 420 = 520.
Therefore, 940 - 420 = 520.
2. 169 - 26:
Step 1: Find the GCF of 169 and 26.
The prime factorization of 169: 13 * 13
The prime factorization of 26: 2 * 13
The common factor is 13.
Step 2: Simplify the numbers.
169 can be written as 13 * 13.
26 can be written as 2 * 13.
Step 3: Perform the subtraction.
(13 * 13) - (2 * 13) = 169 - 26 = 143.
Therefore, 169 - 26 = 143.
3. 15 + 75 - 45:
Step 1: There is no need to find the GCF in this problem.
Step 2: Simplify the numbers.
15 remains the same.
75 can be simplified as 3 * 5 * 5.
45 can be simplified as 3 * 3 * 5.
Step 3: Perform the addition and subtraction.
15 + (3 * 5 * 5) - (3 * 3 * 5) = 15 + 75 - 45 = 45.
Therefore, 15 + 75 - 45 = 45.
4. 48 + 16:
Step 1: There is no need to find the GCF in this problem.
Step 2: The numbers do not need any simplification.
Step 3: Perform the addition.
48 + 16 = 64.
Therefore, 48 + 16 = 64.
5. 17 + 51:
Step 1: There is no need to find the GCF in this problem.
Step 2: The numbers do not need any simplification.
Step 3: Perform the addition.
17 + 51 = 68.
Therefore, 17 + 51 = 68.
In summary, the GCF calculations were not needed for the addition and subtraction problems you mentioned.