The youngest is 5 years old
Step-by-step explanation:
The prime numbers are the numbers that have only two factors
1 and itself
Example: 2, 3, 5, 7, 11, 13, 17, 19, 23, .......
There are six children in a family
- Five of them are respectively 2, 6, 8, 12 and 14 years older than the youngest
- The age of each child is a prime number
We need to find the age of the youngest
Assume that the age of the youngest is x years old
∵ The age of the youngest is x years old
∵ The ages of other children are respectively 2, 6, 8, 12 and 14 years
older than the youngest
∴ The ages of other children are respectively
→ x + 2
→ x + 6
→ x + 8
→ x + 12
→ x + 14
∵ The age of each child is a prime number
- Let us chose x from the list of the prime number above to find the
correct x which makes all the ages are prime
If x = 2
∵ x + 2 = 2 + 2 = 4 ⇒ not prime
∴ x can not be 2
If x = 3
∵ x + 2 = 3 + 2 = 5 ⇒ prime
∵ x + 6 = 3+ 6 = 9 ⇒ not prime
∴ x can not be 3
If x = 5
∵ x + 2 = 5 + 2 = 7 ⇒ prime
∵ x + 6 = 5 + 6 = 11 ⇒ prime
∵ x + 8 = 5 + 8 = 13 ⇒ prime
∵ x + 12 = 5 + 12 = 17 ⇒ prime
∵ x + 14 = 5 + 14 = 19 ⇒ prime
∴ x can be 5
∵ The ages of the children are 5 , 7 , 11 , 13 , 17 , 19
∵ All the ages are prime numbers
∴ The age of the youngest is 5 years
The youngest is 5 years old
Learn more:
You can learn more about prime numbers in brainly.com/question/4550858
#LearnwithBrainly
