Finding the Greatest Common Divisor (GCD)
To find the greatest common divisor (GCD) or "faktor sepunya terbesar (FSTB)" as indicated in the question for a set of numbers, we need to find the largest number that divides each of the numbers without leaving a remainder.
In the image, it looks like you're interested in solving option (e) which lists the numbers 42, 105, and 126. Let's find the GCD of these numbers:
The prime factors for each number are:
- 42 = 2 × 3 × 7
- 105 = 3 × 5 × 7
- 126 = 2 × 3^2 × 7
The GCD is the product of the lowest powers of common primes among these numbers. In this case, the common prime factors are 3 and 7.
So, we take the lowest power of 3 that is common to all, which is 3^1 (since 3^2 is not a factor of 42 and 105), and the lowest power of 7, which is 7^1.
Now multiply these together to find the GCD:
3^1 × 7^1 = 3 × 7 = 21
So, the greatest common divisor of 42, 105, and 126 is 21.
