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Test: Factors - Class 10 MCQ


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10 Questions MCQ Test The Complete SAT Course - Test: Factors

Test: Factors for Class 10 2024 is part of The Complete SAT Course preparation. The Test: Factors questions and answers have been prepared according to the Class 10 exam syllabus.The Test: Factors MCQs are made for Class 10 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Factors below.
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Test: Factors - Question 1

What is the smallest multiple of both 6 and 10?

Detailed Solution for Test: Factors - Question 1

The smallest multiple of both 6 and 10 is their least common multiple (LCM). The prime factors of 6 are 2 and 3, and the prime factors of 10 are 2 and 5. The LCM is the product of the highest powers of all the prime factors: 2 x 3 x 5 = 30.

Test: Factors - Question 2

How many factors does the number 36 have?

Detailed Solution for Test: Factors - Question 2

The prime factorization of 36 is 22 x 32. The number of factors is determined by adding 1 to each exponent in the prime factorization and then multiplying the results: (2 + 1)(2 + 1) = 3 x 3 = 9. 

Test: Factors - Question 3

Which of the following numbers is a multiple of 4 but not a multiple of 8?

Detailed Solution for Test: Factors - Question 3

The multiples of 4 are 4, 8, 12, 16, 20, 24, ... The multiples of 8 are 8, 16, 24, 32, ... The number 12 is a multiple of 4 but not a multiple of 8.

Test: Factors - Question 4

If a is a multiple of 3 and b is a multiple of 4, which of the following must be a multiple of 12?

Detailed Solution for Test: Factors - Question 4

Since a is a multiple of 3, a = 3m for some integer m. Similarly, since b is a multiple of 4, b = 4n for some integer n. Therefore, ab = (3m)(4n) = 12mn. Since mn is an integer, ab is a multiple of 12.

Test: Factors - Question 5

The greatest common factor of 24 and 36 is:

Detailed Solution for Test: Factors - Question 5

The prime factorization of 24 is 23 x 3, and the prime factorization of 36 is 22 x 32. The greatest common factor is the product of the lowest powers of the common prime factors: 22 x 3 = 12.

Test: Factors - Question 6

Which of the following is a prime factor of 84?

Detailed Solution for Test: Factors - Question 6

The prime factorization of 84 is  2 x 2 x 3 x 7.

Test: Factors - Question 7

What are all the factors of 60?

Detailed Solution for Test: Factors - Question 7

Factors of 60 are the numbers that divide evenly into 60. The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

Test: Factors - Question 8

What is the least common multiple of 8, 12, and 16?

Detailed Solution for Test: Factors - Question 8

The least common multiple (LCM) of a set of numbers is the smallest number that is divisible by all of the numbers in the set.
LCM of 8, 12, and 16 by Prime Factorization
Prime factorization of 8, 12, and 16 is (2 × 2 × 2) = 23, (2 × 2 × 3) = 22 × 31, and (2 × 2 × 2 × 2) = 24 respectively. LCM of 8, 12, and 16 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 24 × 31 = 48.
Hence, the LCM of 8, 12, and 16 by prime factorization is 48.

Test: Factors - Question 9

If the greatest common factor of two numbers is 6, and their least common multiple is 60, what are the two numbers?

Detailed Solution for Test: Factors - Question 9

Assume two numbers x and y. We know that the greatest common factor (GCF) of x and y is 6, and the least common multiple (LCM) is 60.
We can use the relationship between GCF and LCM to find x and y. The relationship is given by the formula:
GCF(x, y) * LCM(x, y) = x * y
Substituting the given values, we get:
6 * 60 = x * y
360 = x * y
Now, we need to find two numbers whose product is 360 and whose GCF is 6. One possible pair of numbers is 12 and 30 because 12 * 30 = 360 and GCF(12, 30) = 6.
Therefore, the two numbers are 12 and 30.

Test: Factors - Question 10

Find the greatest common factor of the three numbers: 42, 56, and 70.

Detailed Solution for Test: Factors - Question 10

The prime factors of 42 are 2, 3, and 7.
The prime factors of 56 are 2, 2, 2, and 7.
The prime factors of 70 are 2, 5, and 7.

Taking the common prime factors, we have 2 and 7.
Therefore, the greatest common factor of 42, 56, and 70 is 2 × 7 = 14.

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