Answer:
John's number is 1500
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