G6 Multiples and Factors - Math and Science Olympiad trainer and online tutoring

G6 Multiples and Factors

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1) The HCF of three numbers is 10.
If the numbers are in the ratio 4:5:6, find the numbers.

A) 20, 25, 30

B) 30, 40, 50

C) 40, 50, 60

D) 50, 60, 70

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2) If n is a prime number greater than 3, how many factors does 3n have?

A) 4

B) Cannot be determined

C) 3

D) 2

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3) “a” is a common factor of 12 and 20.
It is also a common multiple of 1 and 4.
“b” is a common factor of 22 and 55.
It is also a common multiple of 1 and 11.
Find the value of a + b + 2.

A) 13

B) 44

C) 15

D) 17

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4) Two numbers have an HCF of 1.
What are such numbers called?

A) Twin primes

B) Perfect numbers

C) Co-prime

D) Composite

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5) Three ropes of lengths 36 m, 48 m, and 60 m are to be cut into equal lengths.
What is the longest length that can be used to cut all ropes exactly?

A) 10 m

B) 12 m

C) 6 m

D) 8 m

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6) Which of the following is a composite number less than 10?

A) 5

B) 3

C) 4

D) 7

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7) “s” is a common factor of 25 and 100.
It is also a common multiple of 5 and 25.
“t” is a common factor of 28 and 70.
It is also a common multiple of 2 and 7.
Find the value of s – t + 3.

A) 350

B) 11

C) 39

D) 14

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8) Which of the following is the smallest 3-digit prime number?

A) 100

B) 101

C) 107

D) 103

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9) Rani has 18 red beads and 30 blue beads.
She wants to make identical sets without leftover beads.

What is the maximum number of sets she can make?

A) 5

B) 6

C) 3

D) 4

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10) The least common multiple of two numbers is 56, and their highest common factor is 7.
If one of the numbers is 28, what is the other number?

A) 35

B) 14

C) 7

D) 21

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11) Raju and Sameer run around a circular track.
Raju completes a round in 36 seconds, Sameer in 48 seconds.

When will they meet at the starting point again?

A) 144

B) 156

C) 120

D) 132

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12) What is the largest 2-digit number that is divisible by both 4 and 6?

A) 88

B) 96

C) 84

D) 92

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13) The least common multiple of two numbers is 48, and their highest common factor is 4.
If one of the numbers is 12, what is the other number?

A) 24

B) 8

C) 16

D) 32

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14) What is the highest power of 2 in the prime factorization of 96?

A) 4

B) 5

C) 6

D) 3

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15) The product of two numbers is 192, and their least common multiple is 48.
What is their highest common factor?

A) 6

B) 4

C) 8

D) 2

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16) What is the LCM of 24 and 36?

A) 60

B) 84

C) 96

D) 72

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17) If p is a prime number greater than 5, how many factors does 5p have?

A) 2

B) 3

C) Cannot be determined

D) 4

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18) The HCF of three numbers is 6.
The ratio is 1:2:3.
What are the numbers?

A) 24, 36, 48

B) 18, 24, 30

C) 12, 18, 24

D) 6, 12, 18

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19) You have numbers from 1 to 50. First, cross out all multiples of 3.
Then, cross out all numbers that have exactly three factors.
How many numbers are remaining?

A) 31

B) 12

C) 42

D) 36

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20) A bus comes every 5 minutes and a train comes every 8 minutes.
If they both arrived at the station at the same time, how many minutes will it be until they both arrive together again?

A) 20

B) 80

C) 13

D) 40

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