Question

find the sum of the first four multiples of the third-largest prime factor occurring in the prime factorization of the number 53064 (IMO)​

Answer 1

$\red{\boxed{\mathfrak\colorbox{grey}{Answer}}}$

Here we have to find first four multiples of the third - largest prime factor occuring in the prime factorization of the number 53064.

➥First we will do the prime factorization of 53064 $\downarrow$

The prime factors are: 2 x 2 x 2 x 3 x 3 x 11 x 67

and here the the third-largest prime factor occurring in the prime factorization of the number 53064 is $\red{67}$.

Now the first four multiples of 67 are

• 67
• 134
• 201
• 268

Now finding the sum of first four multiples of 67

$\boxed{\red{67 + 134 + 201 + 268 = 770}}$

Answer 2

Answer:

Step-by-step explanation:

first the prime factors of 53064

are 3×3×2×2×2×11×67

here the third largest factor is 3 after 11 and 67

now the first four multiples of 3 are 3 , 6, 9 , 12

and the sum of these numbers is 30

and answer is 30