HCF of 870 and 225

HCF of 870 and 225 is the largest possible number that divides 870 and 225 exactly without any remainder. The factors of 870 and 225 are 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870 and 1, 3, 5, 9, 15, 25, 45, 75, 225 respectively. There are 3 commonly used methods to find the HCF of 870 and 225 - prime factorization, long division, and Euclidean algorithm.

Answer: HCF of 870 and 225 is 15.

Explanation:

The HCF of two non-zero integers, x(870) and y(225), is the highest positive integer m(15) that divides both x(870) and y(225) without any remainder.

The methods to find the HCF of 870 and 225 are explained below.

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

HCF of 870 and 225 by Long Division

HCF of 870 and 225 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

• Step 1: Divide 870 (larger number) by 225 (smaller number).
• Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (225) by the remainder (195).
• Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (15) is the HCF of 870 and 225.

HCF of 870 and 225 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 = 870 and Y = 225

• HCF(870, 225) = HCF(225, 870 mod 225) = HCF(225, 195)
• HCF(225, 195) = HCF(195, 225 mod 195) = HCF(195, 30)
• HCF(195, 30) = HCF(30, 195 mod 30) = HCF(30, 15)
• HCF(30, 15) = HCF(15, 30 mod 15) = HCF(15, 0)
• HCF(15, 0) = 15 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 870 and 225 is 15.

HCF of 870 and 225 by Listing Common Factors

• Factors of 870: 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870
• Factors of 225: 1, 3, 5, 9, 15, 25, 45, 75, 225

There are 4 common factors of 870 and 225, that are 1, 3, 5, and 15. Therefore, the highest common factor of 870 and 225 is 15.

☛ Also Check:

• HCF of 404 and 96 = 4
• HCF of 8 and 16 = 8
• HCF of 24 and 36 = 12
• HCF of 441, 567 and 693 = 63
• HCF of 20, 25 and 30 = 5
• HCF of 4 and 16 = 4
• HCF of 26 and 91 = 13

FAQs on HCF of 870 and 225

What is the HCF of 870 and 225?

The HCF of 870 and 225 is 15. To calculate the Highest common factor (HCF) of 870 and 225, we need to factor each number (factors of 870 = 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870; factors of 225 = 1, 3, 5, 9, 15, 25, 45, 75, 225) and choose the highest factor that exactly divides both 870 and 225, i.e., 15.

What is the Relation Between LCM and HCF of 870, 225?

The following equation can be used to express the relation between Least Common Multiple and HCF of 870 and 225, i.e. HCF × LCM = 870 × 225.

How to Find the HCF of 870 and 225 by Prime Factorization?

To find the HCF of 870 and 225, we will find the prime factorization of the given numbers, i.e. 870 = 2 × 3 × 5 × 29; 225 = 3 × 3 × 5 × 5.
⇒ Since 3, 5 are common terms in the prime factorization of 870 and 225. Hence, HCF(870, 225) = 3 × 5 = 15
☛ Prime Number

If the HCF of 225 and 870 is 15, Find its LCM.

HCF(225, 870) × LCM(225, 870) = 225 × 870
Since the HCF of 225 and 870 = 15
⇒ 15 × LCM(225, 870) = 195750
Therefore, LCM = 13050
☛ HCF Calculator

What are the Methods to Find HCF of 870 and 225?

There are three commonly used methods to find the HCF of 870 and 225.

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

How to Find the HCF of 870 and 225 by Long Division Method?

To find the HCF of 870, 225 using long division method, 870 is divided by 225. The corresponding divisor (15) when remainder equals 0 is taken as HCF.