HCF of 1872 and 1320

HCF of 1872 and 1320 is the largest possible number that divides 1872 and 1320 exactly without any remainder. The factors of 1872 and 1320 are 1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 36, 39, 48, 52, 72, 78, 104, 117, 144, 156, 208, 234, 312, 468, 624, 936, 1872 and 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 20, 22, 24, 30, 33, 40, 44, 55, 60, 66, 88, 110, 120, 132, 165, 220, 264, 330, 440, 660, 1320 respectively. There are 3 commonly used methods to find the HCF of 1872 and 1320 - prime factorization, long division, and Euclidean algorithm.

Answer: HCF of 1872 and 1320 is 24.

Explanation:

The HCF of two non-zero integers, x(1872) and y(1320), is the highest positive integer m(24) that divides both x(1872) and y(1320) without any remainder.

The methods to find the HCF of 1872 and 1320 are explained below.

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

HCF of 1872 and 1320 by Listing Common Factors

• Factors of 1872: 1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 36, 39, 48, 52, 72, 78, 104, 117, 144, 156, 208, 234, 312, 468, 624, 936, 1872
• Factors of 1320: 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 20, 22, 24, 30, 33, 40, 44, 55, 60, 66, 88, 110, 120, 132, 165, 220, 264, 330, 440, 660, 1320

There are 8 common factors of 1872 and 1320, that are 1, 2, 3, 4, 6, 8, 12, and 24. Therefore, the highest common factor of 1872 and 1320 is 24.

HCF of 1872 and 1320 by Long Division

HCF of 1872 and 1320 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

• Step 1: Divide 1872 (larger number) by 1320 (smaller number).
• Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (1320) by the remainder (552).
• Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (24) is the HCF of 1872 and 1320.

HCF of 1872 and 1320 by Prime Factorization

Prime factorization of 1872 and 1320 is (2 × 2 × 2 × 2 × 3 × 3 × 13) and (2 × 2 × 2 × 3 × 5 × 11) respectively. As visible, 1872 and 1320 have common prime factors. Hence, the HCF of 1872 and 1320 is 2 × 2 × 2 × 3 = 24.

☛ Also Check:

• HCF of 20 and 30 = 10
• HCF of 8 and 15 = 1
• HCF of 108 and 144 = 36
• HCF of 14 and 16 = 2
• HCF of 4, 8 and 12 = 4
• HCF of 403, 434 and 465 = 31
• HCF of 3 and 9 = 3

FAQs on HCF of 1872 and 1320

What is the HCF of 1872 and 1320?

The HCF of 1872 and 1320 is 24. To calculate the HCF (Highest Common Factor) of 1872 and 1320, we need to factor each number (factors of 1872 = 1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 36, 39, 48, 52, 72, 78, 104, 117, 144, 156, 208, 234, 312, 468, 624, 936, 1872; factors of 1320 = 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 20, 22, 24, 30, 33, 40, 44, 55, 60, 66, 88, 110, 120, 132, 165, 220, 264, 330, 440, 660, 1320) and choose the highest factor that exactly divides both 1872 and 1320, i.e., 24.

What are the Methods to Find HCF of 1872 and 1320?

There are three commonly used methods to find the HCF of 1872 and 1320.

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

How to Find the HCF of 1872 and 1320 by Prime Factorization?

To find the HCF of 1872 and 1320, we will find the prime factorization of the given numbers, i.e. 1872 = 2 × 2 × 2 × 2 × 3 × 3 × 13; 1320 = 2 × 2 × 2 × 3 × 5 × 11.
⇒ Since 2, 2, 2, 3 are common terms in the prime factorization of 1872 and 1320. Hence, HCF(1872, 1320) = 2 × 2 × 2 × 3 = 24
☛ Prime Numbers

What is the Relation Between LCM and HCF of 1872, 1320?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 1872 and 1320, i.e. HCF × LCM = 1872 × 1320.

If the HCF of 1320 and 1872 is 24, Find its LCM.

HCF(1320, 1872) × LCM(1320, 1872) = 1320 × 1872
Since the HCF of 1320 and 1872 = 24
⇒ 24 × LCM(1320, 1872) = 2471040
Therefore, LCM = 102960
☛ Highest Common Factor Calculator

How to Find the HCF of 1872 and 1320 by Long Division Method?

To find the HCF of 1872, 1320 using long division method, 1872 is divided by 1320. The corresponding divisor (24) when remainder equals 0 is taken as HCF.