BCA Prep (Summer Edition) - Chapter 2
How many divisors of 3600 are perfect squares?(JHMMC 2012, challenge)
12
The 5 smallest positive common multiples of18 and 42.
126, 252, 378, 504, 630
How many even numbers are factors of 240?
16
What is the number of factors of the smallest number that ends in a zero and is divisible by 24?(JHMMC2013, Challenge)
16
The LCM of 6, 7, and 8.
168
How many positive whole numbers less than 100 are divisible by 3, but not by 2? (JHMMC 2008 #20)
17
How many positive divisors divide 23 evenly? (JHMMC 2011)
2
How many three-digit numbers re perfect squares? (JHMMC 2008 #39)
22
Find the product of the factors of the following numbers. (Do not calculate the exponents.) a. 225 b. 45
225 = 9 factors 45 = x
What is the smallest number of people that can be broken up both into 15 groups of equal membership and into 48 groups of equal membership?
240
2𝑛2-16 is a prime number. Find all integer values for n. (JHMMC 2011, extra challenge -You may skip this.)
3 or -3
What is the LCM of 6! And 600?
3,600
The GCF for a pair of numbers is 18, and the LCM is 180. If one of the numbers is 90, what is the other number?
36
The product of two numbers is 315 and their GCF is 3. What is their LCM?
36
How many odd numbers are factors of 240?
4
How many perfect squares are factors of 360? (Hint: consider counting the number of "even power" choices for each prime factor)
4
The number 1126 can be factored as the product of two primes. Find their sum. (JHMMC 2012)
565
A pair of positive integers 𝑎and 𝑏is such that their GCF is 5 and their LCM is 55. Find the smallest possible value of 𝑎+𝑏. (JHMMC 2008 #27)
60
Ying and Catherine walked to the store together to buy some pencils. Ying bought 40 pencils and Catherine bought 24. If each package of pencils sold at the store contain the same number of pencils, what is the largest possible number of pencils in a package?
8
13. Find the sum of the factors of the following numbers. a. 108 b. 378 c. 408
960
Jenny places a total of 18 red Easter eggs in several green baskets and a total of 24 orange Easter eggs in some blue baskets. Each basket contains the same number of eggs and there are at least 4 eggs in each basket. (a) How many eggs did Jenny put in each basket? (b) How many green baskets were used?
a = x b = x
Find all 2-digit positive integers which have exactly 12 factors?(challenge)
x
Find all the common multiples of 6 and 15 that are between 1 and 100.
x
Find all the positive common divisors of 12 and 18.
x
Find all the positive common divisors of 14 and 42.
x
Find all the positive common divisors of 20 and 35.
x
Find all the positive common divisors of 23 and 36.
x
Find the LCM of 8, 12, and 14.
x
Find the LCM of 9 and 24.
x
Find the largest divisor of 2800 that is a perfect square. (JHMMC 2008 #17)
x
How many factors does each of the following numbers have? a. 72, b. 180, c. 210, d. 112
x
How many multiples of 17 are there between 23 and 227? (JHMMC 2008 #18)
x
How many positive factors does 7! have?
x
What is the smallest positive integer that has exactly 10 factors?(challenge)
x
What is the smallest positive integer that has exactly 6 factors?
x
What is the smallest positive integer with exactly 7 factors? (JHMMC 2014 #26)
x
x
x
The product of the factors of 30 is equal to 2𝑥3𝑥5𝑥. Find x.
x =4
