HCF of 84 and 90

HCF of 84 and 90 is the largest possible number that divides 84 and 90 exactly without any remainder. The factors of 84 and 90 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 and 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 respectively. There are 3 commonly used methods to find the HCF of 84 and 90 - long division, Euclidean algorithm, and prime factorization.

Answer: HCF of 84 and 90 is 6.

Explanation:

The HCF of two non-zero integers, x(84) and y(90), is the highest positive integer m(6) that divides both x(84) and y(90) without any remainder.

Let's look at the different methods for finding the HCF of 84 and 90.

• Long Division Method
• Prime Factorization Method
• Listing Common Factors

HCF of 84 and 90 by Long Division

HCF of 84 and 90 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

• Step 1: Divide 90 (larger number) by 84 (smaller number).
• Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (84) by the remainder (6).
• Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (6) is the HCF of 84 and 90.

HCF of 84 and 90 by Prime Factorization

Prime factorization of 84 and 90 is (2 × 2 × 3 × 7) and (2 × 3 × 3 × 5) respectively. As visible, 84 and 90 have common prime factors. Hence, the HCF of 84 and 90 is 2 × 3 = 6.

HCF of 84 and 90 by Listing Common Factors

• Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
• Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

There are 4 common factors of 84 and 90, that are 1, 2, 3, and 6. Therefore, the highest common factor of 84 and 90 is 6.

☛ Also Check:

• HCF of 1650 and 847 = 11
• HCF of 12 and 15 = 3
• HCF of 0 and 6 = 6
• HCF of 4 and 8 = 4
• HCF of 72 and 84 = 12
• HCF of 20, 25 and 30 = 5
• HCF of 72, 108 and 180 = 36

FAQs on HCF of 84 and 90

What is the HCF of 84 and 90?

The HCF of 84 and 90 is 6. To calculate the Highest common factor (HCF) of 84 and 90, we need to factor each number (factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84; factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90) and choose the highest factor that exactly divides both 84 and 90, i.e., 6.

What is the Relation Between LCM and HCF of 84, 90?

The following equation can be used to express the relation between LCM and HCF of 84 and 90, i.e. HCF × LCM = 84 × 90.

How to Find the HCF of 84 and 90 by Long Division Method?

To find the HCF of 84, 90 using long division method, 90 is divided by 84. The corresponding divisor (6) when remainder equals 0 is taken as HCF.

What are the Methods to Find HCF of 84 and 90?

There are three commonly used methods to find the HCF of 84 and 90.

• By Listing Common Factors
• By Prime Factorization
• By Long Division

If the HCF of 90 and 84 is 6, Find its LCM.

HCF(90, 84) × LCM(90, 84) = 90 × 84
Since the HCF of 90 and 84 = 6
⇒ 6 × LCM(90, 84) = 7560
Therefore, LCM = 1260
☛ HCF Calculator

How to Find the HCF of 84 and 90 by Prime Factorization?

To find the HCF of 84 and 90, we will find the prime factorization of the given numbers, i.e. 84 = 2 × 2 × 3 × 7; 90 = 2 × 3 × 3 × 5.
⇒ Since 2, 3 are common terms in the prime factorization of 84 and 90. Hence, HCF(84, 90) = 2 × 3 = 6
☛ What is a Prime Number?