Factors and HCF Challenge

Find all the factors of 24.

• 1, 2, 4, 8, 16, 24

• 5, 10, 15, 20, 25

• 2, 3, 5, 7, 11, 13

• 1, 2, 3, 4, 6, 8, 12, 24

Answer explanation

The factors of 24 are the numbers that divide evenly into 24 without leaving a remainder. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.

Calculate the highest common factor of 36 and 48.

• 18

• 6

• 24

• 12

Answer explanation

The highest common factor of 36 and 48 is 12. To find the highest common factor, you can list the factors of each number and find the largest one they have in common, which in this case is 12.

Determine the prime factors of 30.

• 1, 4, 7

• 2, 3, 5

• 5, 10, 15

• 2, 3, 6

Answer explanation

The prime factors of 30 are 2, 3, and 5. Therefore, the correct choice is 2, 3, 5.

What is the prime factorization of 72?

• 2x2x2x2x3

• 2x2x3

• 2x2x2x3x3

• 2x3x2x3x2x3x2x4

Answer explanation

The prime factorization of 72 is 2x2x2x3x3. Therefore, the correct choice is 2x2x2x3x3.

Find the HCF of 54 and 72 using the prime factorization method.

• 10

• 12

• 8

• 6

Answer explanation

To find the HCF of 54 and 72 using prime factorization, first factorize both numbers: 54 = 2 * 3^3 and 72 = 2^3 * 3^2. Then, identify the common prime factors and multiply them: HCF = 2 * 3 = 6.

Calculate the highest common factor of 45 and 75.

• 15

• 10

• 25

• 20

Answer explanation

The highest common factor of 45 and 75 is 15. This is because 15 is the largest number that can evenly divide both 45 and 75.

What are the prime factors of 48?

• 4, 8

• 2, 3

• 3, 6

• 2, 4

Answer explanation

The prime factors of 48 are 2 and 3. 48 = 2^4 * 3^1, so the prime factors are 2 and 3.

Find the highest common factor of the number of apples James has, which is 84, and the number of oranges he has, which is 126.

• 63

• 42

• 21

• 105

Answer explanation

The highest common factor of 84 and 126 is 42. It is the largest number that divides both 84 and 126 without leaving a remainder.

Find the highest common factor between the number of apples Jackson has, which is 36, and the number of oranges Isla has, which is 54.

• 18

• 6

• 24

• 12

What is the prime factorization of 90?

• 2x3x3x5

• 2x2x3x3x5

• 2x2x2x3x5

• 3x3x3x3x3