What is the greatest common factor (GCF) of 48 and 64?
12
16
24
32
The Greatest Common Factor (GCF) of 48 and 64 is 16. To find the GCF, we list the prime factors of both numbers. The prime factors of 48 are 2 × 2 × 2 × 2 × 3 (or (2⁴ × 3)), and the prime factors of 64 are 2 × 2 × 2 × 2 × 2 × 2 (or (2⁶)). The common prime factor is 2, and the highest power of 2 that is common to both numbers is (2⁴). Therefore, the GCF is (2⁴) which equals 16.
Step 1: Find the prime factors of each number.
Prime factors of 48: 2 x 2 x 2 x 2 x 3
Prime factors of 64: 2 x 2 x 2 x 2 x 2 x 2
Step 2: Identify the common prime factors.
Step 3: Multiply the common prime factors.
GCF = (2⁴) = 16
So, the greatest common factor of 48 and 64 is 16.
Step 1: Divide the larger number by the smaller number
64 ÷ 48 = 1 with a remainder of 16.
Step 2: Replace the larger number with the smaller number, and the smaller number with the remainder
Now, we have 48 and 16.
Step 3: Repeat the division
48 ÷ 16 = 3 with a remainder of 0.
Step 4: When the remainder is 0, the divisors is the GCF
The last non-zero remainder is 16. So, the GCF of 48 and 64 is 16.
To find the Greatest Common Factor (GCF) of 48 and 64 by listing common factors, follow these steps:
Step 1: List the factors of each number
Factors of 48:
Factors of 64:
Step 2: Identify the common factors
Common factors of 48 and 64:
Step 3: Determine the greatest common factor
The largest common factor is 16. Therefore, the GCF of 48 and 64 is 16.
You can find the GCF by using the long division method or by listing common factors.
The GCF is useful in simplifying fractions and solving problems involving divisibility.
Yes, simplifying 48/64 using the GCF of 16 gives 3/4.
The product of the GCF and LCM of two numbers equals the product of the numbers.
By repeatedly applying the division method until the remainder is zero.
Yes, you can extend the method to find the GCF of more than two numbers.
The Greatest Common Factor (GCF) of 48 and 64 is 16. To find the GCF, we list the prime factors of both numbers. The prime factors of 48 are 2 × 2 × 2 × 2 × 3 (or (2⁴ × 3)), and the prime factors of 64 are 2 × 2 × 2 × 2 × 2 × 2 (or (2⁶)). The common prime factor is 2, and the highest power of 2 that is common to both numbers is (2⁴). Therefore, the GCF is (2⁴) which equals 16.
Prime Factorization Method
Long Division Method
Listing Common Factors
Step 1: Find the prime factors of each number.
Prime factors of 48: 2 x 2 x 2 x 2 x 3
Prime factors of 64: 2 x 2 x 2 x 2 x 2 x 2
Step 2: Identify the common prime factors.
Common prime factors: 2 x 2 x 2 x 2 = (2⁴)
Step 3: Multiply the common prime factors.
GCF = (2⁴) = 16
So, the greatest common factor of 48 and 64 is 16.
Step 1: Divide the larger number by the smaller number
64 ÷ 48 = 1 with a remainder of 16.
Step 2: Replace the larger number with the smaller number, and the smaller number with the remainder
Now, we have 48 and 16.
Step 3: Repeat the division
48 ÷ 16 = 3 with a remainder of 0.
Step 4: When the remainder is 0, the divisors is the GCF
The last non-zero remainder is 16. So, the GCF of 48 and 64 is 16.
To find the Greatest Common Factor (GCF) of 48 and 64 by listing common factors, follow these steps:
Step 1: List the factors of each number
Factors of 48:
1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 64:
1, 2, 4, 8, 16, 32, 64
Step 2: Identify the common factors
Common factors of 48 and 64:
1, 2, 4, 8, 16
Step 3: Determine the greatest common factor
The largest common factor is 16. Therefore, the GCF of 48 and 64 is 16.
You can find the GCF by using the long division method or by listing common factors.
The GCF is useful in simplifying fractions and solving problems involving divisibility.
Yes, simplifying 48/64 using the GCF of 16 gives 3/4.
The product of the GCF and LCM of two numbers equals the product of the numbers.
By repeatedly applying the division method until the remainder is zero.
Yes, you can extend the method to find the GCF of more than two numbers.
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What is the greatest common factor (GCF) of 48 and 64?
12
16
24
32
Which of the following is a common factor of both 48 and 64?
6
10
16
20
If you divide 48 by its GCF with 64, what is the quotient?
3
4
6
8
The GCF of 48 and 64 is also a factor of which of the following numbers?
80
100
128
150
What is the smallest multiple of the GCF of 48 and 64 that is greater than 50?
64
80
96
112
What is the least common multiple (LCM) of 48 and 64 if the GCF is 16?
192
128
96
80
Which number is not divisible by the GCF of 48 and 64?
32
48
64
40
If the GCF of two numbers is 16 and one of the numbers is 48, what could be the other number?
32
64
96
128
What is the GCF of 48 and 64 if we add 16 to each number?
16
32
48
64
Which of the following numbers has the same GCF with 48 as it does with 64?
24
56
72
80
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