The HCF of 10224 and 9648 is 144. The value which divides the 10224 and 9648 equally is the HCF. The factors of 10224 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 the factors of 9648 are 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. The value of HCF of 10224 and 9648 calculated using prime factorisation, long division and listing common factors are shown here in a simple way by the faculty at BYJU’S.
Also read: Highest common factor
What is the HCF of 10224 and 9648?
The answer to this question is 144. The various methods to find the HCF of 10224 and 9648 are given in this article. The HCF of 10224 and 9648 is 144 which divides both the numbers exactly.
How to Find HCF of 10224 and 9648?
The methods used to find the HCF of 10224 and 9648 are:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 10224 and 9648 by Prime Factorisation Method
The prime factorisation of 10224 and 9648 is:
10224 = 2 × 2 × 2 × 2 × 3 × 3 × 71
9648 = 2 × 2 × 2 × 2 × 3 × 3 × 67
Common prime factors of 10224 and 9648 = 2 × 2 × 2 × 2 × 3 × 3 = 144
Therefore, HCF (10224, 9648) = 144
HCF of 10224 and 9648 by Long Division Method
To find the HCF, we have to divide the number 10224 by 9648. The HCF of 10224 and 9648 is the divisor value we obtain when the remainder is zero.
No further division can be done.
Hence, HCF (10224, 9648) = 144
HCF of 10224 and 9648 by Listing Common Factors
The HCF of 10224 and 9648 by listing the common factors is:
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
There are 15 common factors of 10224 and 9648, and they are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72 and 144.
Therefore, the highest common factor of 10224 and 9648 is 144.
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Video Lesson on Properties of HCF and LCM
HCF of 10224 and 9648 Solved Example
Question: If the product of two numbers = 98641152 and HCF = 144, find the LCM.
Solution:
Given
Product of two numbers = 98641152
HCF = 144
HCF × LCM = Product of two numbers
144 × LCM = 98641152
LCM = 98641152/144
LCM = 685008
Hence, the LCM is 685008.
Frequently Asked Questions on HCF of 10224 and 9648
What is the HCF of 10224 and 9648 if the LCM is 685008?
Given
LCM = 685008
LCM × HCF = 10224 × 9648
HCF = (10224 × 9648)/685008
HCF = 98641152/685008
HCF = 144
Find the HCF of 10224 and 9648 using the long division method.
What are the methods used to find the HCF of 10224 and 9648?
What is the HCF of 10224 and 9648?
Show the relation between HCF and LCM of 10224 and 9648.
The relation between HCF and LCM of 10224 and 9648 is
HCF × LCM = 10224 × 9648
HCF × LCM = 98641152
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