The highest common factor of 16, 32, 40 is
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To find the highest common factor (HCF) of these numbers, we need to find the factors they have in common and identify the highest one.
First, we list the prime factors of each number:
16 = 2 x 2 x 2 x 2
32 = 2 x 2 x 2 x 2 x 2
40 = 2 x 2 x 2 x 5
We can see that all three numbers have 2 raised to the power of 2 as a common factor. They also all have at least one more factor of 2 in common. Therefore, the HCF of these numbers is 2 x 2 x 2 = 8.
Alternatively, we can use the division method to find the HCF:
16 divided by 8 = 2 with a remainder of 0
32 divided by 8 = 4 with a remainder of 0
40 divided by 8 = 5 with a remainder of 0
Since all three numbers can be evenly divided by 8, this is their highest common factor.
To find the highest common factor (HCF) of 16, 32, and 40, we can use the method of prime factorization. Here is the step-by-step process:
1. Begin by finding the prime factorization of each number:
- Prime factorization of 16: 2 x 2 x 2 x 2 = 2^4
- Prime factorization of 32: 2 x 2 x 2 x 2 x 2 = 2^5
- Prime factorization of 40: 2 x 2 x 2 x 5 = 2^3 x 5
2. Write down the factorization of each number using their common prime factors:
- 16: 2^4
- 32: 2^5
- 40: 2^3 x 5
3. Determine the highest power of each common prime factor:
- The highest power of 2 is 2^4
- The highest power of 5 is 5^0 (since it only appears in the factorization of 40)
4. Multiply the common prime factors with the highest powers:
- HCF = 2^4 x 5^0
- HCF = 16
Therefore, the highest common factor (HCF) of 16, 32, and 40 is 16.