To find the greatest number which exactly divides 14, 21, and 42, we need to determine the greatest common divisor (GCD) of these three numbers. Here's a step-by-step solution to find the GCD:
1. Prime Factorization:
- First, let's find the prime factors of each number.
- 14 can be factored into [tex]\( 2 \times 7 \)[/tex].
- 21 can be factored into [tex]\( 3 \times 7 \)[/tex].
- 42 can be factored into [tex]\( 2 \times 3 \times 7 \)[/tex].
2. Common Prime Factors:
- Identify the common prime factors in all three factorizations.
- The common prime factor for 14, 21, and 42 is [tex]\( 7 \)[/tex].
3. GCD Calculation:
- Since 7 is the only common prime factor, it is the greatest common divisor that appears in all three numbers.
Putting this all together, the greatest number which exactly divides 14, 21, and 42 is 7.
