GCF of 16 and 42

GCF of 16 and 42 is the largest possible number that divides 16 and 42 exactly without any remainder. The factors of 16 and 42 are 1, 2, 4, 8, 16 and 1, 2, 3, 6, 7, 14, 21, 42 respectively. There are 3 commonly used methods to find the GCF of 16 and 42 - Euclidean algorithm, prime factorization, and long division.

Answer: GCF of 16 and 42 is 2.

Explanation:

The GCF of two non-zero integers, x(16) and y(42), is the greatest positive integer m(2) that divides both x(16) and y(42) without any remainder.

Let's look at the different methods for finding the GCF of 16 and 42.

• Using Euclid's Algorithm
• Long Division Method
• Listing Common Factors

GCF of 16 and 42 by Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 42 and Y = 16

• GCF(42, 16) = GCF(16, 42 mod 16) = GCF(16, 10)
• GCF(16, 10) = GCF(10, 16 mod 10) = GCF(10, 6)
• GCF(10, 6) = GCF(6, 10 mod 6) = GCF(6, 4)
• GCF(6, 4) = GCF(4, 6 mod 4) = GCF(4, 2)
• GCF(4, 2) = GCF(2, 4 mod 2) = GCF(2, 0)
• GCF(2, 0) = 2 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 16 and 42 is 2.

GCF of 16 and 42 by Long Division

GCF of 16 and 42 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

• Step 1: Divide 42 (larger number) by 16 (smaller number).
• Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (16) by the remainder (10).
• Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the GCF of 16 and 42.

GCF of 16 and 42 by Listing Common Factors

• Factors of 16: 1, 2, 4, 8, 16
• Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42

There are 2 common factors of 16 and 42, that are 1 and 2. Therefore, the greatest common factor of 16 and 42 is 2.

☛ Also Check:

• GCF of 15 and 24 = 3
• GCF of 32 and 80 = 16
• GCF of 42, 28 and 70 = 14
• GCF of 27 and 30 = 3
• GCF of 36 and 100 = 4
• GCF of 56 and 35 = 7
• GCF of 12 and 9 = 3

FAQs on GCF of 16 and 42

What is the GCF of 16 and 42?

The GCF of 16 and 42 is 2. To calculate the greatest common factor of 16 and 42, we need to factor each number (factors of 16 = 1, 2, 4, 8, 16; factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42) and choose the greatest factor that exactly divides both 16 and 42, i.e., 2.

If the GCF of 42 and 16 is 2, Find its LCM.

GCF(42, 16) × LCM(42, 16) = 42 × 16
Since the GCF of 42 and 16 = 2
⇒ 2 × LCM(42, 16) = 672
Therefore, LCM = 336
☛ GCF Calculator

What is the Relation Between LCM and GCF of 16, 42?

The following equation can be used to express the relation between LCM and GCF of 16 and 42, i.e. GCF × LCM = 16 × 42.

How to Find the GCF of 16 and 42 by Prime Factorization?

To find the GCF of 16 and 42, we will find the prime factorization of the given numbers, i.e. 16 = 2 × 2 × 2 × 2; 42 = 2 × 3 × 7.
⇒ Since 2 is the only common prime factor of 16 and 42. Hence, GCF (16, 42) = 2.
☛ What is a Prime Number?

How to Find the GCF of 16 and 42 by Long Division Method?

To find the GCF of 16, 42 using long division method, 42 is divided by 16. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 16 and 42?

There are three commonly used methods to find the GCF of 16 and 42.

• By Euclidean Algorithm
• By Long Division
• By Prime Factorization