Test:Factors & Mulitples - 1 - CTET & State TET MCQ

Multiples of 10: 10, 20, 30, 40, 50, 60, 70,...
Multiples of 12: 12, 24, 36, 48, 60, 72,...
∴ The smallest whole number divisible by both 10 and 12 is 60.

L.C.M. of 12 and 18 is 36.
∴ The required number of stamps is the largest multiple of 36, less than 500.
500 ÷ 36 = 13 R 32 as 36 × 13 = 468 and 36 × 14 = 504.
Thus, the required number of stamps = 468.

12 = 2 × 2 × 3
24 = 2 × 2 × 2 × 3
36 = 2 × 2 × 3 × 3
L.C.M. of 12, 24 and 36  = 2 × 2 × 3 × 2 × 3 = 72.

26, 39, and 65 are multiples of 13, whereas 71 is not a multiple of 13.

Example: 2 is a factor of 6 and 6 is a multiple of 2.

Co-prime numbers have no common factor other than1, So, their L.C.M. is their product.

Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36.
Factors of 144 are 1, 2, 3, 4, 6 8, 9, 12, 16, 18, 24, 36, 48, 72 and 144.
The common factors of 36 and 144 are 1, 2, 3, 4, 6, 9, 12, 18 and 36 of which 36 is the highest.
∴ H.C.F of 36 and 144 is 36.

The prime numbers that differ by 2 are called twin primes. e.g., 3, 5 as both 3 and 5 are prime numbers and their difference is 2.

Since, 14 is a multiple of 7 : 10 is a multiple of 5.
∴ Required answer = 7 : 14 : : 5 : 10.

12, 249, and 18 are multiples of 6, whereas 43 is not a multiple of 6.

48 = 3 × 16 is a multiple of 16.
64 = 4 × 16 is a multiple of 16.
80 = 5 × 16 is a multiple of 16.
44 = 2 × 2 × 11 is not a multiple of 16.
42 = 6 × 7 is not a multiple of 16.
66 = 3 × 2 × 11 is not a multiple of 16.
86 = 2 × 43 is not a multiple of 16.
46 = 2 × 23 is not a multiple of 16.
68 = 2 × 2 × 17 is not a multiple of 16.
88 = 2 × 2 × 2 × 11 is not a multiple of 16.

L.C.M. of 45 and 50 is 5 × 9 × 10 = 450 = P.
∴ 10P + 100 = 450 × 10 + 100 = 4500 + 100 = 4600.

• The two numbers which have only 1 as their common factor are called co-primes.
• For Example: Factors of 5  are 1, 5 Factors of 3 are 1, 3 Common factors is 1. So they are co-prime numbers.

Factors of 8: 1, 2, 4, 8
Multiples of 2: 2, 4, 6, 8, 10, 12.....
So, 6 is a multiple of 2 but not a factor of 8.

The rule is to multiply each term by 3 to get the next term.
So, 54 × 3 = 162 is the next number in the sequence.

Co-prime numbers have no common factor other than 1. So, their H.C.F is 1.

• Three pairs of prime numbers whose difference is 2 are (5, 7), (11, 13) and (17, 19).
• A pair of prime numbers whose difference is 2 are called twin primes.
• The alternative names given to twin primes are prime twin or prime pair.

Factors of 45: 1, 3, 5, 9, 15, 45
Multiples of 3: 3, 6, 9, 12, 15, 18.....
So, 5 is a factor of 45 but not a multiple of 3.

Since, 4 is a factor of 24 and 3 is a factor of 9.
∴ Required Answer = 3 : 9 : : 4 : 24.

63 = 9 × 7.