GCF of 30 and 45
GCF of 30 and 45
To find the GCF (Greatest Common Factor) of 30 and 45, we start by listing the prime factors of each number. The prime factors of 30 are 2, 3, and 5 (since 30 = 2 × 3 × 5). For 45, the prime factors are 3 and 5 (since 45 = 3 × 3 × 5). Next, we identify the common prime factors between the two numbers, which are 3 and 5. Multiplying these common factors together gives us the GCF. Therefore, the GCF of 30 and 45 is 3 × 5 = 15.
GCF of 30 and 45
GCF of 30 and 45 is 15.
Methods to Find GCF of 30 and 45
- Prime Factorization Method
- Long Division Method
- Listing Common Factors
GCF of 30 and 45 by Prime Factorization Method
To find the GCF (Greatest Common Factor) of 30 and 45 using the prime factorization method, follow these steps:
To find the GCF (Greatest Common Factor) of 30 and 45 using the prime factorization method, follow these steps:
Prime Factorization:
30: The prime factors of 30 are 2, 3, and 5.
30 = 2 × 3 × 5
45: The prime factors of 45 are 3 and 5.
45 = 3 × 3 × 5
Identify Common Factors:
Both numbers have the common prime factors of 3 and 5.
Calculate the GCF:
Multiply the common prime factors together.
GCF = 3 × 5 = 15
Thus, the GCF of 30 and 45 using the prime factorization method is 15.
GCF of 30 and 45 by Long Division Method.
Divide the larger number by the smaller number:
Divide 45 by 30.
45 ÷ 30 = 1 remainder 15
Replace the larger number with the smaller number and the smaller number with the remainder:
Now, divide 30 by the remainder 15.
30 ÷ 15 = 2 remainder 0
Continue the process until the remainder is 0:
Since the remainder is now 0, the divisor at this step is the GCF.
Therefore, the GCF of 30 and 45 using the long division method is 15.
GCF of 30 and 45 by Listing Common Factors
List the factors of each number:
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Factors of 45: 1, 3, 5, 9, 15, 45
Identify the common factors:
Common factors of 30 and 45: 1, 3, 5, 15
Determine the greatest common factor:
The largest common factor is 15.
Therefore, the GCF of 30 and 45 by listing common factors is 15.
What is the greatest common factor of 30 and 45 brainly?
The greatest common factor (GCF) of 30 and 45 is 15. This is the largest number that divides both 30 and 45 without leaving a remainder.
Can the GCF of 30 and 45 be greater than 30?
No, the GCF is always less than or equal to the smaller number.
What are the common factors of 30 and 45?
The common factors are 1, 3, 5, and 15.
How does finding the GCF help in simplifying fractions?
The GCF is used to simplify fractions by dividing the numerator and the denominator by the GCF.
Are 30 and 45 relatively prime?
No, they are not relatively prime because their GCF is 15, not 1.
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