HCF of 504 and 980

HCF of 504 and 980 is the largest possible number that divides 504 and 980 exactly without any remainder. The factors of 504 and 980 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504 and 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980 respectively. There are 3 commonly used methods to find the HCF of 504 and 980 - Euclidean algorithm, long division, and prime factorization.

Answer: HCF of 504 and 980 is 28.

Explanation:

The HCF of two non-zero integers, x(504) and y(980), is the highest positive integer m(28) that divides both x(504) and y(980) without any remainder.

The methods to find the HCF of 504 and 980 are explained below.

• Prime Factorization Method
• Listing Common Factors
• Using Euclid's Algorithm

HCF of 504 and 980 by Prime Factorization

Prime factorization of 504 and 980 is (2 × 2 × 2 × 3 × 3 × 7) and (2 × 2 × 5 × 7 × 7) respectively. As visible, 504 and 980 have common prime factors. Hence, the HCF of 504 and 980 is 2 × 2 × 7 = 28.

HCF of 504 and 980 by Listing Common Factors

• Factors of 504: 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504
• Factors of 980: 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980

There are 6 common factors of 504 and 980, that are 1, 2, 4, 7, 14, and 28. Therefore, the highest common factor of 504 and 980 is 28.

HCF of 504 and 980 by Euclidean Algorithm

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

Here X = 980 and Y = 504

• HCF(980, 504) = HCF(504, 980 mod 504) = HCF(504, 476)
• HCF(504, 476) = HCF(476, 504 mod 476) = HCF(476, 28)
• HCF(476, 28) = HCF(28, 476 mod 28) = HCF(28, 0)
• HCF(28, 0) = 28 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 504 and 980 is 28.

☛ Also Check:

• HCF of 777 and 1147 = 37
• HCF of 81 and 237 = 3
• HCF of 1260 and 7344 = 36
• HCF of 510 and 92 = 2
• HCF of 12, 15 and 18 = 3
• HCF of 2 and 4 = 2
• HCF of 9 and 12 = 3

FAQs on HCF of 504 and 980

What is the HCF of 504 and 980?

The HCF of 504 and 980 is 28. To calculate the Highest common factor (HCF) of 504 and 980, we need to factor each number (factors of 504 = 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504; factors of 980 = 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980) and choose the highest factor that exactly divides both 504 and 980, i.e., 28.

How to Find the HCF of 504 and 980 by Prime Factorization?

To find the HCF of 504 and 980, we will find the prime factorization of the given numbers, i.e. 504 = 2 × 2 × 2 × 3 × 3 × 7; 980 = 2 × 2 × 5 × 7 × 7.
⇒ Since 2, 2, 7 are common terms in the prime factorization of 504 and 980. Hence, HCF(504, 980) = 2 × 2 × 7 = 28
☛ Prime Number

If the HCF of 980 and 504 is 28, Find its LCM.

HCF(980, 504) × LCM(980, 504) = 980 × 504
Since the HCF of 980 and 504 = 28
⇒ 28 × LCM(980, 504) = 493920
Therefore, LCM = 17640
☛ Highest Common Factor Calculator

What is the Relation Between LCM and HCF of 504, 980?

The following equation can be used to express the relation between LCM and HCF of 504 and 980, i.e. HCF × LCM = 504 × 980.

What are the Methods to Find HCF of 504 and 980?

There are three commonly used methods to find the HCF of 504 and 980.

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

How to Find the HCF of 504 and 980 by Long Division Method?

To find the HCF of 504, 980 using long division method, 980 is divided by 504. The corresponding divisor (28) when remainder equals 0 is taken as HCF.