Sonali bought 24 red beans, 32 yellow beads and 48 blue beads to be made into necklaces. If they are to be made into necklaces such that there is an equal number of red, yellow and blue beads in every necklace and no bead remaining after they are made into necklace, what is the maximum number of such necklaces that can be made?
GCD(24,32,48) = 8
So, 8 necklaces, each with 3,4,6 of the respective colors.
To find the maximum number of necklaces that can be made with an equal number of red, yellow, and blue beads, we need to find the greatest common divisor (GCD) of the numbers of each color.
First, let's find the GCD of 24, 32, and 48.
The prime factors of 24 are 2 × 2 × 2 × 3.
The prime factors of 32 are 2 × 2 × 2 × 2 × 2.
The prime factors of 48 are 2 × 2 × 2 × 2 × 3.
To find the GCD, we take the common prime factors with the lowest exponent.
The GCD of 24, 32, and 48 is 2 × 2 × 2 = 8.
Therefore, the maximum number of necklaces that can be made is 8.
To find the maximum number of necklaces that can be made with equal numbers of red, yellow, and blue beads, we need to find the greatest common divisor (GCD) of the three quantities: 24, 32, and 48.
Step 1: Find the prime factors of each quantity.
24: 2^3 * 3
32: 2^5
48: 2^4 * 3
Step 2: Identify the common factors among the three quantities.
The only common factor among all three quantities is 2^3, which is equal to 8.
Step 3: Multiply these common factors.
Multiplying the common factor 8 by 1, we get 8 * 1 = 8.
Therefore, the maximum number of necklaces that can be made with equal numbers of red, yellow, and blue beads is 8.