What is the Greatest Common Factor (GCF) of 21 and 28?
3
5
7
9
The greatest common factor (GCF) of 21 and 28 is 7. By analyzing the factors of both numbers, we find that 21 has factors 1, 3, 7, and 21, while 28 has factors 1, 2, 4, 7, 14, and 28. The largest factor they share in common is 7, making it the greatest common factor. This indicates that 7 is the largest numbers that divides both 21 and 28 without leaving a remainder. Therefore, the GCF of 21 and 28 is 7.
To find the greatest common factor (GCF) of 21 and 28 using the prime factorization method:
Step 1: Prime factorize both numbers.
For 21: 21=3×7
For 28: 28 = 2²×7
Step 2: Identify the common prime factors and their lowest powers. Both 21 and 28 have a common prime factor of 7, but 28 also has an additional factor of 2².
Step 3: Multiply the common prime factors with their lowest powers.
GCF = 7
Therefore, the greatest common factor (GCF) of 21 and 28 by prime factorization method is 7.
To find the greatest common factor (GCF) of 21 and 28 using the long division method:
Step 1: Divide the larger number (28) by the smaller number (21). 28 ÷ 21 =1 with a remainder of 7.
Step 2: Then, divide the divisor (21) by the remainder (7). 21 ÷ 7 = 3.2
Step 3: Continue dividing until there is no remainder.
7 ÷ 3 = 2 with a remainder of 1.
3 ÷ 1= 3.
1 ÷ 1 = 1.
Step 4: The last divisors before reaching 1 is the greatest common factor (GCF). GCF = 1 × 7 = 7.
Therefore, the greatest common factor (GCF) of 21 and 28 by the long division method is 7.
To find the greatest common factor (GCF) of 21 and 28 by listing common factors:
Step 1: List the factors of each number.
Factors of 21: 1, 3, 7, 21
Factors of 28: 1, 2, 4, 7, 14, 28
Step 2: Identify the common factors. Common factors: 1, 7
Step 3: Determine the greatest common factor. GCF = 7
Therefore, the greatest common factor (GCF) of 21 and 28 by listing common factors is 7.
You can calculate the GCF of 21 and 28 using methods such as prime factorization, listing common factors, or long division.
No, the GCF cannot be larger than both numbers. It is always a factor of both numbers.
The GCF is the product of the common prime factors raised to their lowest powers.
The GCF can be used to reduce fractions to their simplest form by dividing both the numerator and denominator by the GCF.
The GCF of 21 and 28 is the greatest common divisor, as it represents the largest divisor common to both numbers.
Yes, knowing the GCF can help in finding common factors or simplifying problems involving multiples of 21 and 28.
The greatest common factor (GCF) of 21 and 28 is 7. By analyzing the factors of both numbers, we find that 21 has factors 1, 3, 7, and 21, while 28 has factors 1, 2, 4, 7, 14, and 28. The largest factor they share in common is 7, making it the greatest common factor. This indicates that 7 is the largest numbers that divides both 21 and 28 without leaving a remainder. Therefore, the GCF of 21 and 28 is 7.
To find the greatest common factor (GCF) of 21 and 28 using the prime factorization method:
Step 1: Prime factorize both numbers.
For 21: 21=3×7
For 28: 28 = 2²×7
Step 2: Identify the common prime factors and their lowest powers. Both 21 and 28 have a common prime factor of 7, but 28 also has an additional factor of 2².
Step 3: Multiply the common prime factors with their lowest powers.
GCF = 7
Therefore, the greatest common factor (GCF) of 21 and 28 by prime factorization method is 7.
To find the greatest common factor (GCF) of 21 and 28 using the long division method:
Step 1: Divide the larger number (28) by the smaller number (21). 28 ÷ 21 =1 with a remainder of 7.
Step 2: Then, divide the divisor (21) by the remainder (7). 21 ÷ 7 = 3.2
Step 3: Continue dividing until there is no remainder.
7 ÷ 3 = 2 with a remainder of 1.
3 ÷ 1= 3.
1 ÷ 1 = 1.
Step 4: The last divisors before reaching 1 is the greatest common factor (GCF). GCF = 1 × 7 = 7.
Therefore, the greatest common factor (GCF) of 21 and 28 by the long division method is 7.
To find the greatest common factor (GCF) of 21 and 28 by listing common factors:
Step 1: List the factors of each number.
Factors of 21: 1, 3, 7, 21
Factors of 28: 1, 2, 4, 7, 14, 28
Step 2: Identify the common factors. Common factors: 1, 7
Step 3: Determine the greatest common factor. GCF = 7
Therefore, the greatest common factor (GCF) of 21 and 28 by listing common factors is 7.
You can calculate the GCF of 21 and 28 using methods such as prime factorization, listing common factors, or long division.
No, the GCF cannot be larger than both numbers. It is always a factor of both numbers.
The GCF is the product of the common prime factors raised to their lowest powers.
The GCF can be used to reduce fractions to their simplest form by dividing both the numerator and denominator by the GCF.
The GCF of 21 and 28 is the greatest common divisor, as it represents the largest divisor common to both numbers.
Yes, knowing the GCF can help in finding common factors or simplifying problems involving multiples of 21 and 28.
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What is the Greatest Common Factor (GCF) of 21 and 28?
3
5
7
9
Which of the following numbers is a common factor of both 21 and 28?
2
5
7
9
What is the smallest prime factor of the GCF of 21 and 28?
2
3
5
7
How many factors does the GCF of 21 and 28 have?
1
2
3
4
If you subtract the GCF of 21 and 28 from 21, what is the result?
12
14
21
28
What is the GCF of 21 and 28 multiplied by 2?
7
14
21
28
Which of the following numbers is not divisible by the GCF of 21 and 28?
14
21
28
35
The GCF of 21 and 28 is what fraction of 21?
1/3
1/2
1/7
1/4
The GCF of 21 and 28 is also a factor of which of the following numbers?
14
20
35
49
The difference between the GCF of 21 and 28 and the number 3 is?
2
4
5
6
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