HCF Questions

HCF, or Highest Common Factor, is a simple but important math concept. It’s like finding the biggest number that can evenly divide two or more numbers. Knowing how to do this can be really handy in solving various math problems.

In this article, we’re going to walk you through a bunch of easy HCF questions. 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.

Join us as we explore the world of 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 HCF 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 HCF 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, and 7. The highest among them is 7. So, the HCF of 35 and 70 is 7.

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 HCF 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 HCF 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.

Related Links:

• Factorization
• Fractions
• Long Division Method

Question 11: Liam has 54 stamps. He wants to distribute them equally among his friends. What is the maximum number of friends he can distribute the stamps to, so that each friend gets the same number of stamps?

Solution:

To find the maximum number of friends Liam can distribute the stamps to equally, we need to find the HCF of 54.
Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
The HCF of 54 is 6.
Therefore, Liam can distribute the stamps to 6 friends, and each friend will get the same number of stamps.

Question 12: Susan has 96 flowers. She wants to make flower bouquets with an equal number of flowers in each bouquet. What is the maximum number of flowers she can put in each bouquet?

Solution:

To find the maximum number of flowers Susan can put in each bouquet with an equal number of flowers, we need to find the HCF of 96.
Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
The HCF of 96 is 48.
Therefore, Susan can put 48 flowers in each bouquet.

Question 13: Emma has 90 candies. She wants to divide them into boxes. What is the maximum number of candies she can put in each box if she wants to ensure that each box has the same number of candies?

Solution:

To find the maximum number of candies Emma can put in each box with the same number of candies, we need to find the HCF of 90.
Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
The HCF of 90 is 90.
Therefore, Emma can put 90 candies in each box.

Question 14: A school library has 120 storybooks. 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?

Solution:

To find the maximum number of classrooms the school library can distribute the books to equally, we need to find the HCF of 120.
Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
The HCF of 120 is 120.
Therefore, the school library can distribute the books to classrooms, and each classroom will get the same number of books.

Question 15: 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 16: 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 17: 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 18: 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 19: 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 20: 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 21: 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 22: 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 23: 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 25: 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 36 and 48.

Question 2: Determine the HCF of the fractions 3/5 and 9/15.

Question 3: Calculate the HCF of 0.3 and 0.6.

Question 4: John has 24 red apples, 36 green apples, and 48 yellow apples. How many apples can he arrange in equal rows with no apples left over?

Question 5: A farmer has 18 cows, 24 sheep, and 36 goats. What is the largest number of animals he can put in each pen, so that each pen has the same number of animals?