Some of my factors are 2, 4, 8 and 16. One of my multiples is 64. What number can I be?
32 probably i think
To find the number that satisfies the given criteria, we need to determine the number that has 2, 4, 8, and 16 as factors and 64 as one of its multiples.
Since all the given factors are powers of 2, we can conclude that the number in question is also a power of 2.
To find the number, we can start by identifying the largest power of 2 from the given factors, which is 16.
Now, let's keep multiplying 16 by 2 to find the multiples until we reach 64:
16 x 2 = 32
32 x 2 = 64
Therefore, the number that satisfies the given criteria is 64.
To find the number that matches the given factors and has a multiple of 64, we can use the concept of prime factorization.
Prime factorization is the process of expressing a number as a product of its prime factors.
Let's break down the given factors into their prime factors:
2 = 2
4 = 2 × 2
8 = 2 × 2 × 2
16 = 2 × 2 × 2 × 2
Now, let's do the same for the multiple:
64 = 2 × 2 × 2 × 2 × 2 × 2
To find the number you can be, we need to combine the prime factors of the factors and compare them with the prime factorization of 64.
From the given factors, we found that the common prime factor is 2, and it appears 4 times in the factor 16. However, since the number 64 has six 2's in its prime factorization, you need 2 more 2's to make them equal.
Therefore, the number you can be is 16 × 2 × 2 = 64.
So, the answer is 64.