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QUIZ FOR FUNDAMNETAL THEOREM OF ARITHMETIC

Total questions: 25

Worksheet time: 22mins

Name
Class
Date
1.

Also called the unique factorization theorem states that every positive integer (except 1) can be produced in only one unique way apart from rearrangement as a product of one or more prime numbers.

(a)  

2.

According to Fundamental Theorem of Arithmetic 13915 is a

(a)  

3.

Using the fundamental theorem of arithmetic, find the HCF of 34, 39 and 91

(a)  

4.

find the HCF of 816 and 170 using Fundamental Theorem of Arithmetic.

(a)  

5.

Using the fundamental theorem of arithmetic find the LCM of 816 and 170.

(a)  

6.

The prime factorization of 1575 is

(a)  

7.

The smallest prime number is

(a)  

8.

The GCF of 140, 20, and 350 using the fundamental theorem of arithmetic is

(a)  

9.

The exponent of 5 in the prime factorization of 3750 is

(a)  

10.

Fundamental Theorem of Arithmetic is also known as

(a)  

11.

By the fundamental theorem of arithmetic, every integer greater than 1 is either a/an   (a)   or can be expressed in the form of primes.

12.

John has a rectangular garden with a length of 60 feet and a width of 75 feet. He wants to install a sprinkler system that covers the entire garden evenly. What is the maximum length of piping he can use without any waste?

(a)  

13.

Sarah is planning a flower arrangement using vases with 36 roses and 48 tulips. She wants to create identical arrangements with the maximum number of flowers in each vase. What is the maximum number of flowers she can place in each vase?

(a)  

14.

A company is packaging products into boxes, with 80 items in each box and 120 items in each crate. What is the maximum number of items that can be in each box without any left-over items?

(a)  

15.

A carpenter is cutting wooden boards into equal lengths for a project. The lengths of the boards are 96 inches and 120 inches. What is the maximum length the carpenter can cut without any waste?

(a)  

16.

Find the GCD of 180 and 225 using prime factorization.

(a)  

17.

Determine the GCD of 72 and 144 using prime factorization

(a)  

18.

In a formula racing competition the time taken by two racing cars A and B to complete 1 round of the track is 30 minutes and 45 minutes respectively. After how much time will the cars meet again at the starting point?

(a)  

19.

By the fundamental theorem of arithmetic, every (a)   number can be factored as a product of primes, which is unique excluding the order of prime factors.

20.

By the fundamental theorem of arithmetic, every integer greater than 1 is either a/an ______number or the product of _____factors.



(a)  

21.

The LCM of three numbers is 240, and their GCD is 12. If two numbers are 48 and 120, find the third.

(a)  

22.

The LCM of two numbers is 60, and their GCD is 5. If one number is 15, find the other.

(a)  

23.

The LCM of three numbers is 400, and their GCD is 20. If two numbers are 80 and 200, find the third.

(a)  

24.

A train schedule for two different routes is such that Train A arrives every 20 days, and Train B arrives every 28 days. What is the least number of days before both trains arrive on the same day?

(a)  

25.

The LCM of three numbers is 400, and their GCD is 20. If two numbers are 80 and 200, find the third.

(a)