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HCF of 10224 and 9648

HCF of 10224 and 9648 is the largest possible number that divides 10224 and 9648 exactly without any remainder. The factors of 10224 and 9648 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 71, 72, 142, 144, 213, 284, 426, 568, 639, 852, 1136, 1278, 1704, 2556, 3408, 5112, 10224 and 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 67, 72, 134, 144, 201, 268, 402, 536, 603, 804, 1072, 1206, 1608, 2412, 3216, 4824, 9648 respectively. There are 3 commonly used methods to find the HCF of 10224 and 9648 - prime factorization, long division, and Euclidean algorithm.

1.	HCF of 10224 and 9648
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 10224 and 9648?

Answer: HCF of 10224 and 9648 is 144.

Explanation:

The HCF of two non-zero integers, x(10224) and y(9648), is the highest positive integer m(144) that divides both x(10224) and y(9648) without any remainder.

Methods to Find HCF of 10224 and 9648

The methods to find the HCF of 10224 and 9648 are explained below.

Using Euclid's Algorithm
Prime Factorization Method
Long Division Method

HCF of 10224 and 9648 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 = 10224 and Y = 9648

HCF(10224, 9648) = HCF(9648, 10224 mod 9648) = HCF(9648, 576)
HCF(9648, 576) = HCF(576, 9648 mod 576) = HCF(576, 432)
HCF(576, 432) = HCF(432, 576 mod 432) = HCF(432, 144)
HCF(432, 144) = HCF(144, 432 mod 144) = HCF(144, 0)
HCF(144, 0) = 144 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 10224 and 9648 is 144.

HCF of 10224 and 9648 by Prime Factorization

Prime factorization of 10224 and 9648 is (2 × 2 × 2 × 2 × 3 × 3 × 71) and (2 × 2 × 2 × 2 × 3 × 3 × 67) respectively. As visible, 10224 and 9648 have common prime factors. Hence, the HCF of 10224 and 9648 is 2 × 2 × 2 × 2 × 3 × 3 = 144.

HCF of 10224 and 9648 by Long Division

HCF of 10224 and 9648 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 10224 (larger number) by 9648 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (9648) by the remainder (576).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (144) is the HCF of 10224 and 9648.

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HCF of 10224 and 9648 Examples

Example 1: The product of two numbers is 98641152. If their HCF is 144, what is their LCM?

Solution:

Given: HCF = 144 and product of numbers = 98641152
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 98641152/144
Therefore, the LCM is 685008.
Example 2: Find the HCF of 10224 and 9648, if their LCM is 685008.

Solution:

∵ LCM × HCF = 10224 × 9648
⇒ HCF(10224, 9648) = (10224 × 9648)/685008 = 144
Therefore, the highest common factor of 10224 and 9648 is 144.
Example 3: Find the highest number that divides 10224 and 9648 exactly.

Solution:

The highest number that divides 10224 and 9648 exactly is their highest common factor, i.e. HCF of 10224 and 9648.
⇒ Factors of 10224 and 9648:
- Factors of 10224 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 71, 72, 142, 144, 213, 284, 426, 568, 639, 852, 1136, 1278, 1704, 2556, 3408, 5112, 10224
- Factors of 9648 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 67, 72, 134, 144, 201, 268, 402, 536, 603, 804, 1072, 1206, 1608, 2412, 3216, 4824, 9648
Therefore, the HCF of 10224 and 9648 is 144.

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FAQs on HCF of 10224 and 9648

What is the HCF of 10224 and 9648?

The HCF of 10224 and 9648 is 144. To calculate the Highest common factor (HCF) of 10224 and 9648, we need to factor each number (factors of 10224 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 71, 72, 142, 144, 213, 284, 426, 568, 639, 852, 1136, 1278, 1704, 2556, 3408, 5112, 10224; factors of 9648 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 67, 72, 134, 144, 201, 268, 402, 536, 603, 804, 1072, 1206, 1608, 2412, 3216, 4824, 9648) and choose the highest factor that exactly divides both 10224 and 9648, i.e., 144.

How to Find the HCF of 10224 and 9648 by Prime Factorization?

To find the HCF of 10224 and 9648, we will find the prime factorization of the given numbers, i.e. 10224 = 2 × 2 × 2 × 2 × 3 × 3 × 71; 9648 = 2 × 2 × 2 × 2 × 3 × 3 × 67.
⇒ Since 2, 2, 2, 2, 3, 3 are common terms in the prime factorization of 10224 and 9648. Hence, HCF(10224, 9648) = 2 × 2 × 2 × 2 × 3 × 3 = 144
☛ What is a Prime Number?

How to Find the HCF of 10224 and 9648 by Long Division Method?

To find the HCF of 10224, 9648 using long division method, 10224 is divided by 9648. The corresponding divisor (144) when remainder equals 0 is taken as HCF.

If the HCF of 9648 and 10224 is 144, Find its LCM.

HCF(9648, 10224) × LCM(9648, 10224) = 9648 × 10224
Since the HCF of 9648 and 10224 = 144
⇒ 144 × LCM(9648, 10224) = 98641152
Therefore, LCM = 685008
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What are the Methods to Find HCF of 10224 and 9648?

There are three commonly used methods to find the HCF of 10224 and 9648.

By Euclidean Algorithm
By Long Division
By Prime Factorization

What is the Relation Between LCM and HCF of 10224, 9648?

The following equation can be used to express the relation between Least Common Multiple and HCF of 10224 and 9648, i.e. HCF × LCM = 10224 × 9648.

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