## GCF 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.

## GCF of 21 and 28

### GCF of 21 and 28 is 7.

## GCF of 21 and 28 by Prime Factorization Method.

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.

## GCF of 21 and 28 by Long Division Method.

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.

## GCF of 21 and 28 by Listing Common Factors.

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.

## How do you calculate the GCF of 21 and 28?

You can calculate the GCF of 21 and 28 using methods such as prime factorization, listing common factors, or long division.

## Can the GCF of 21 and 28 be larger than both numbers?

No, the GCF cannot be larger than both numbers. It is always a factor of both numbers.

## What is the relationship between the GCF of 21 and 28 and their prime factorization?

The GCF is the product of the common prime factors raised to their lowest powers.

## How does the GCF of 21 and 28 help in simplifying fractions?

The GCF can be used to reduce fractions to their simplest form by dividing both the numerator and denominator by the GCF.

## How does the GCF of 21 and 28 relate to the concept of greatest common divisor?

The GCF of 21 and 28 is the greatest common divisor, as it represents the largest divisor common to both numbers.

## Can you use the GCF of 21 and 28 to solve problems involving factors and multiples?

Yes, knowing the GCF can help in finding common factors or simplifying problems involving multiples of 21 and 28.