## John is thinking of a number. He gives the following 3 clues. “My number has 125 as a factor. My number is a multiple of 30. My number is b

Question

John is thinking of a number. He gives the following 3 clues. “My number has 125 as a factor. My number is a multiple of 30. My number is between 800 and 2000.” What is John’s number?

Please answer correctly

in progress 0
2 weeks 2021-09-12T08:37:51+00:00 1 Answer 0

## Answers ( )

1. Answer:

John’s number is 1500

Step-by-step explanation:

* Lets explain how to solve the problem

– Factors of a number are the numbers you multiply to get the number

– Ex: Factors of 12 are 1 × 12 , 2 × 6 , 3 × 4

– The factors of a number smaller than or equal the number

– Multiple of a number is that number multiplied by an integer

– Ex: 2, 4, 6, 8, and 10 are multiples of 2

– The multiples of a number greater than or equal the number

* Lets solve the number

– John is thinking of a number

– He gives the following 3 clues

# The number has 125 as a factor

# The number is a multiple of 30

# The number is between 800 and 2000

∵ 125 is a factor of the number

– Assume that the number is 125 (its factors 1 , 5 , 25 , 125)

∵ The number is a multiple of 30

– Assume the number is 30 (the first multiple of 30)

– To solve the problem lets find the lowest common multiple of 125

and 30 by using prime numbers only

∵ The prime factors of 125 = 5 × 5 × 5

∵ The prime factors of 30 = 2 × 3 × 5

– L.C.M of the two numbers is the product of their prime factors

without reputation

∴ L.C.M = 5 × 5 × 5 × 2 × 3 = 750

∵ 750 has 125 as a factor

∵ 750 is a multiple of 30

– But 750 is not between 800 and 2000

∴ Find a multiple of 750 and between 800 and 2000

∵ 2 × 750 = 1500

* lets check the three clues

∵ 1500 has 125 as a factor

∵ 1500 is a multiple of 30

∵ 1500 is between 800 and 2000

∴ John’s number is 1500