Answer :
To find the Highest Common Factor (HCF) of the numbers 24, 40, and 64, we can use a method called prime factorization. Here's how you can do it step-by-step:
1. Prime Factorization: Break down each number into its prime factors.
- 24:
- 24 can be divided by 2 to get 12.
- 12 can be divided by 2 to get 6.
- 6 can be divided by 2 to get 3.
- 3 is a prime number, so it cannot be divided further.
- Therefore, the prime factors of 24 are [tex]\(2^3 \times 3\)[/tex].
- 40:
- 40 can be divided by 2 to get 20.
- 20 can be divided by 2 to get 10.
- 10 can be divided by 2 to get 5.
- 5 is a prime number, so it cannot be divided further.
- Therefore, the prime factors of 40 are [tex]\(2^3 \times 5\)[/tex].
- 64:
- 64 can be divided by 2 to get 32.
- 32 can be divided by 2 to get 16.
- 16 can be divided by 2 to get 8.
- 8 can be divided by 2 to get 4.
- 4 can be divided by 2 to get 2.
- 2 is a prime number, so it cannot be divided further.
- Therefore, the prime factors of 64 are [tex]\(2^6\)[/tex].
2. Identify Common Prime Factors:
- All three numbers have the common prime factor of 2 in their factorizations.
3. Find the Lowest Power of Common Factors:
- The lowest power of 2 common to all factorizations is [tex]\(2^3\)[/tex].
4. Calculate the HCF:
- The HCF is [tex]\(2^3 = 8\)[/tex].
Therefore, the Highest Common Factor of 24, 40, and 64 is 8.
1. Prime Factorization: Break down each number into its prime factors.
- 24:
- 24 can be divided by 2 to get 12.
- 12 can be divided by 2 to get 6.
- 6 can be divided by 2 to get 3.
- 3 is a prime number, so it cannot be divided further.
- Therefore, the prime factors of 24 are [tex]\(2^3 \times 3\)[/tex].
- 40:
- 40 can be divided by 2 to get 20.
- 20 can be divided by 2 to get 10.
- 10 can be divided by 2 to get 5.
- 5 is a prime number, so it cannot be divided further.
- Therefore, the prime factors of 40 are [tex]\(2^3 \times 5\)[/tex].
- 64:
- 64 can be divided by 2 to get 32.
- 32 can be divided by 2 to get 16.
- 16 can be divided by 2 to get 8.
- 8 can be divided by 2 to get 4.
- 4 can be divided by 2 to get 2.
- 2 is a prime number, so it cannot be divided further.
- Therefore, the prime factors of 64 are [tex]\(2^6\)[/tex].
2. Identify Common Prime Factors:
- All three numbers have the common prime factor of 2 in their factorizations.
3. Find the Lowest Power of Common Factors:
- The lowest power of 2 common to all factorizations is [tex]\(2^3\)[/tex].
4. Calculate the HCF:
- The HCF is [tex]\(2^3 = 8\)[/tex].
Therefore, the Highest Common Factor of 24, 40, and 64 is 8.
