The Fundamental Theorem of Arithmetic

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?

• 60 minutes

• 90 minutes

• 68 minutes

• 110 minutes

Answer explanation

This time can be calculated by finding the L.C.M of the time taken by each.

30 = 2 × 3 × 5

45 = 3 × 3 × 5

The L.C.M is 90.

Thus, both cars will meet at the starting point after 90 minutes.

The LCM and HCF of 120 and 480 will be

• 480, 80

• 720, 120

• 1080, 120

• 480, 120

The LCM of 16 and 216 is 432. The HCF will be

• 6

• 4

• 8

• 2

The LCM and HCF of two numbers are 2079 and 9 respectively. If one number is 693, the other number is

• 27

• 18

• 36

• 29

The prime factor of 324 is

• 4 x 9 x 9

• 2 x 2 x 3 x 3 x 9

• 2 x 2 x 3 x 3 x 3 x 3

• 4 x 3 x 3 x 3 x 3

If a and b are two composite numbers, which of the following is true

• a x LCM = b x HCF

• HCF x LCM = a x b

• b x LCM = a x HCF

• None of these

The prime factorization of Natural Number is ______ except for the ______ of its factors.

• Unique, Order

• Order, Unique

• Similar, Order

• None of the above

The Fundamental Theorem of Arithmetic says that every composite number can be factorized as a

• roduct of Natural Numbers

• Product of Integers

• Product of Real Numbers

• Product of Primes

The HCF of three consecutive Natural Number is

• -1

• 0

• 1

• 2

The product of prime factors of 5005 is

• 5 x 7 x 143

• 5 x 1001

• 5 x 7 x 11 x 13

• 11 x 13 x 35