GCF of 42, 28 and 70

GCF of 42, 28 and 70 is the largest possible number that divides 42, 28 and 70 exactly without any remainder. The factors of 42, 28 and 70 are (1, 2, 3, 6, 7, 14, 21, 42), (1, 2, 4, 7, 14, 28) and (1, 2, 5, 7, 10, 14, 35, 70) respectively. There are 3 commonly used methods to find the GCF of 42, 28 and 70 - Euclidean algorithm, prime factorization, and long division.

Answer: GCF of 42, 28 and 70 is 14.

Explanation:

The GCF of three non-zero integers, x(42), y(28) and z(70), is the greatest positive integer m(14) that divides x(42), y(28) and z(70) without any remainder.

Let's look at the different methods for finding the GCF of 42, 28 and 70.

• Prime Factorization Method
• Long Division Method
• Using Euclid's Algorithm

GCF of 42, 28 and 70 by Prime Factorization

Prime factorization of 42, 28 and 70 is (2 × 3 × 7), (2 × 2 × 7) and (2 × 5 × 7) respectively. As visible, 42, 28 and 70 have common prime factors. Hence, the GCF of 42, 28 and 70 is 2 × 7 = 14.

GCF of 42, 28 and 70 by Long Division

GCF of 42, 28 and 70 can be represented as GCF of (GCF of 42, 28) and 70. GCF(42, 28, 70) can be thus calculated by first finding GCF(42, 28) using long division and thereafter using this result with 70 to perform long division again.

• Step 1: Divide 42 (larger number) by 28 (smaller number).
• Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (28) by the remainder (14). Repeat this process until the remainder = 0.
  ⇒ GCF(42, 28) = 14.
• Step 3: Now to find the GCF of 14 and 70, we will perform a long division on 70 and 14.
• Step 4: For remainder = 0, divisor = 14 ⇒ GCF(14, 70) = 14

Thus, GCF(42, 28, 70) = GCF(GCF(42, 28), 70) = 14.

GCF of 42, 28 and 70 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.

GCF(42, 28, 70) = GCF(GCF(42, 28), 70)

• GCF(42, 28) = GCF(28, 42 mod 28) = GCF(28, 14)
• GCF(28, 14) = GCF(14, 28 mod 14) = GCF(14, 0)
• GCF(14, 0) = 14 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Steps for GCF(14, 70)

• GCF(70, 14) = GCF(14, 70 mod 14) = GCF(14, 0)
• GCF(14, 0) = 14 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 42, 28 and 70 is 14.

☛ Also Check:

• GCF of 16 and 60 = 4
• GCF of 16 and 56 = 8
• GCF of 12 and 28 = 4
• GCF of 54 and 32 = 2
• GCF of 35 and 50 = 5
• GCF of 24 and 42 = 6
• GCF of 84 and 42 = 42

FAQs on GCF of 42, 28 and 70

What is the GCF of 42, 28 and 70?

The GCF of 42, 28 and 70 is 14. To calculate the GCF of 42, 28 and 70, we need to factor each number (factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42; factors of 28 = 1, 2, 4, 7, 14, 28; factors of 70 = 1, 2, 5, 7, 10, 14, 35, 70) and choose the greatest factor that exactly divides 42, 28 and 70, i.e., 14.

How to Find the GCF of 42, 28 and 70 by Prime Factorization?

To find the GCF of 42, 28 and 70, we will find the prime factorization of given numbers, i.e. 42 = 2 × 3 × 7; 28 = 2 × 2 × 7; 70 = 2 × 5 × 7.
⇒ Since 2, 7 are common terms in the prime factorization of 42, 28 and 70. Hence, GCF(42, 28, 70) = 2 × 7 = 14
☛ What are Prime Numbers?

Which of the following is GCF of 42, 28 and 70? 14, 105, 105, 118, 115, 100

GCF of 42, 28, 70 will be the number that divides 42, 28, and 70 without leaving any remainder. The only number that satisfies the given condition is 14.

What is the Relation Between LCM and GCF of 42, 28 and 70?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 42, 28 and 70, i.e. GCF(42, 28, 70) = [(42 × 28 × 70) × LCM(42, 28, 70)]/[LCM(42, 28) × LCM (28, 70) × LCM(42, 70)].
☛ GCF Calculator

What are the Methods to Find GCF of 42, 28 and 70?

There are three commonly used methods to find the GCF of 42, 28 and 70.

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