Highest Common Factor (HCF) or Greatest common divisor (GCD) is a simple but important math concept. It's like finding the biggest number that evenly divides two or more numbers. Knowing how to do this can be handy in solving various math problems.
The HCF or GCD of two numbers is defined as the largest number that can exactly divide both the numbers.
In this article, we're going to solve a bunch of HCF questions. This will help you to improve your understanding of the concept Whether you're a student getting ready for a math test or just someone who wants to get better at math, these questions and explanations will make it super easy to understand.
Read: Highest Common Factors
HCF Questions with Solutions
Question 1: Find out the HCF of 36 and 48.
Solution:
Using the division method for HCFHence, HCF = 12
Question 2: Find out the HCF of 24 and 36.
Solution:
Let's find out the HCF of 24 and 36 by division method,Therefore, HCF = 2 × 2 × 3 = 12
Question 3: Find the GCD of 18 and 27.
Solution:
To find the HCF of 18 and 27,
we can list the factors of each number:
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 27: 1, 3, 9, 27
The common factors of 18 and 27 are 1, 3, and 9.
The highest among them is 9. So, the HCF of 18 and 27 is 9.
Question 4: Calculate the GCD of 35 and 70.
Solution:
To find the HCF of 35 and 70, we can list the factors of each number:
Factors of 35: 1, 5, 7, 35
Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70
The common factors of 35 and 70 are 1, 5, 7 and 35.
The highest among them is 35. So, the HCF of 35 and 70 is 35.
Question 5: Determine the HCF of 42 and 56.
Solution:
To find the HCF of 42 and 56, we can list the factors of each number:
Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
The common factors of 42 and 56 are 1, 2, 7, and 14.
The highest among them is 14. So, the HCF of 42 and 56 is 14.
Question 6: Find the GCD of 16 and 24.
Solution:
To find the HCF of 16 and 24, we can list the factors of each number:
Factors of 16: 1, 2, 4, 8, 16
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
The common factors of 16 and 24 are 1, 2, 4, and 8.
The highest among them is 8. So, the HCF of 16 and 24 is 8.
Question 7: Calculate the HCF of 75 and 105.
Solution:
To find the HCF of 75 and 105, we can list the factors of each number:
Factors of 75: 1, 3, 5, 15, 25, 75
Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105
The common factors of 75 and 105 are 1, 3, 5, and 15.
The highest among them is 15. So, the HCF of 75 and 105 is 15.
Question 8: Determine the GCD of 48 and 72.
Solution:
To find the HCF of 48 and 72, we can list the factors of each number:
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
The common factors of 48 and 72 are 1, 2, 3, 4, 6, 8, 12, and 24.
The highest among them is 24. So, the HCF of 48 and 72 is 24.
Question 9: Find the HCF of 63 and 84.
Solution:
To find the HCF of 63 and 84, we can list the factors of each number:
Factors of 63: 1, 3, 7, 9, 21, 63
Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The common factors of 63 and 84 are 1, 3, 7, and 21.
The highest among them is 21. So, the HCF of 63 and 84 is 21.
Question 10: Calculate the HCF of 120 and 150.
Solution:
To find the HCF of 120 and 150, we can list the factors of each number:
Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
The common factors of 120 and 150 are 1, 2, 3, 5, 6, 10, 15, and 30.
The highest among them is 30. So, the HCF of 120 and 150 is 30.
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Question 11: The HCF of two numbers is 9, and their product is 567. If one of the numbers is 63, what is the second number?
Solution:
Let the second number be 'x'.
We know that HCF × Product of two numbers = LCM × Second number.
So, 9 × 567 = x × 63
Solving for 'x', we get: x = 81.
Therefore, the second number is 81.
Question 12: The HCF of three numbers is 12, and their LCM is 180. Two of the numbers are 36 and 60. What is the third number?
Solution:
Let the third number be 'y'.
We know that HCF × LCM = Product of three numbers.
So, 12 × 180 = 36 × 60 × y
Solving for 'y', we get: y = 30.
Therefore, the third number is 30.
Question 13: The HCF of four numbers is 15, and their LCM is 840. Three of the numbers are 35, 70, and 105. What is the fourth number?
Solution:
Let the fourth number be 'z'.
We know that HCF × LCM = Product of four numbers.
So, 15 × 840 = 35 × 70 × 105 × z
Solving for 'z', we get: z = 24.
Therefore, the fourth number is 24.
Question 14: Find the HCF of 4/10 and 8/20.
Solution:
To find the HCF of fractions, first simplify the fractions:
4/10 = (4 × 1)/(10 × 1) = 4/10 = 2/5
8/20 = (8 × 1)/(20 × 1) = 8/20 = 2/5
The fractions are already simplified.
Therefore, the HCF of 4/10 and 8/20 is 2/5.
Question 15: Find the HCF of 6/9 and 12/18.
Solution:
To find the HCF of fractions, first simplify the fractions:
6/9 = (6 × 1)/(9 × 1) = 6/9 = 2/3
12/18 = (12 × 1)/(18 × 1) = 12/18 = 2/3
The fractions are already simplified.
Therefore, the HCF of 6/9 and 12/18 is 2/3.
Question 16: Find the HCF of 9/12 and 15/20.
Solution:
To find the HCF of fractions, first simplify the fractions:
9/12 = (9 × 1)/(12 × 1) = 9/12 = 3/4
15/20 = (15 × 1)/(20 × 1) = 15/20 = 3/4
The fractions are already simplified.
Therefore, the HCF of 9/12 and 15/20 is 3/4.
Question 17: Find the HCF of 2/7 and 10/35.
Solution:
To find the HCF of fractions, first simplify the fractions:
2/7 = (2 × 1)/(7 × 1) = 2/7
10/35 = (10 × 1)/(35 × 1) = 10/35 = 2/7
The fractions are already simplified.
Therefore, the HCF of 2/7 and 10/35 is 2/7.
Question 18: Find the HCF of 8/24 and 12/36.
Solution:
To find the HCF of fractions, first simplify the fractions:
8/24 = (8 × 1)/(24 × 1) = 8/24 = 1/3
12/36 = (12 × 1)/(36 × 1) = 12/36 = 1/3
The fractions are already simplified.
Therefore, the HCF of 8/24 and 12/36 is 1/3.
Question 19: Find the HCF of 0.4 and 0.8.
Solution:
To find the HCF of decimals, multiply the decimals by an appropriate power of 10 to make them whole numbers:
0.4 × 10 = 4
0.8 × 10 = 8
Now, find the HCF of the whole numbers, which is 4.
Therefore, the HCF of 0.4 and 0.8 is 0.4.
Question 20: Find the HCF of 0.25 and 0.5.
Solution:
To find the HCF of decimals, multiply the decimals by an appropriate power of 10 to make them whole numbers:
0.25 × 100 = 25
0.5 × 100 = 50
Now, find the HCF of the whole numbers, which is 25.
Therefore, the HCF of 0.25 and 0.5 is 0.25.
Practice Questions on HCF
Question 1. Find the Highest Common Factor (HCF) of 45 and 60.
Question 2. Determine the HCF of the fractions 2/7 and 8/14.
Question 3. Calculate the HCF of 0.45 and 0.9.
Question 4. Sarah has 48 oranges, 60 bananas, and 84 apples. What is the maximum number of groups of fruits that she can arrange so that there are equal fruits of each type in every group with no fruits left over?
Question 5. A baker has 24 chocolate cupcakes, 36 vanilla cupcakes, and 48 strawberry cupcakes. What is the largest number of boxes that can be made, so that each box has the same number of cupcakes?
Question 6: Susan has 96 roses and 60 sunflowers. She wants to make flower bouquets with an equal number of flowers in each bouquet. What is the maximum number of bouquet she can make?
Question 7: Emma has 90 candies and 160 chocolates. She wants to divide them into boxes. What is the maximum number of boxes she can make if she wants to ensure that each box has the same number of candies?
Question 8. Find the Highest Common Factor (HCF) of 125, 75, and 35.
Question 9: A school library has 120 storybooks and 250 Academic Books. They want to distribute them to classrooms equally. What is the maximum number of classrooms they can distribute the books to so that each classroom gets the same number of books?
Answers to Practice Problems | ||
|---|---|---|
Ans 1: HCF = 15 | Ans 2: HCF = 2/7 | Ans 3: HCF = 0.45 |
Ans 4: 12 groups | Ans 5: 12 boxes | Ans 6: 12 Bouquets |
Ans 7: 10 boxes | Ans 8: 5 | Ans 9: 10 classrooms |
What is HCF, and what makes it significant?
The biggest integer that can divide two or more numbers equally is called the HCF, or highest common factor. It's crucial for a variety of mathematical applications, including ratio problem solving and fraction simplification.
How is the HCF of two numbers calculated?
One can determine the HCF of two integers by applying techniques like the division method, the prime factorization method, or a list of common factors. The HCF is the most significant shared factor.
How does LCM and HCF differ from one another?
HCF (Highest Common Factor) is the largest number that divides two or more numbers, while LCM (Least Common Multiple) is the smallest number that is a multiple of two or more numbers.
What is the HCF of two prime numbers ?
The HCF of two prime numbers is always 1, as their only common factor is 1.