Question

Find the cube root by prime factorization of 294×252

Answer 1

Answer:

Step-by-step explanation:

294 = 2 × 3 × 72;  

252 = 22 × 32 × 7;

Take all the common prime factors, by the lowest exponents.

Greatest (highest) common factor (divisor):  

gcf, gcd (294; 252) = 2 × 3 × 7 = 42;

Using Euclid's algorithm:

Step 1. Divide the larger number by the smaller one:  

294 ÷ 252 = 1 + 42;

Step 2. Divide the smaller number by the above operation's remainder:  

252 ÷ 42 = 6 + 0;

At this step, the remainder is zero, so we stop:  

42 is the number we were looking for, the last remainder that is not zero.  

This is the greatest common factor (divisor).

Greatest (highest) common factor (divisor):  

gcf, gcd (294; 252) = 42 = 2 × 3 × 7;

Final answer:  

Greatest (highest) common factor (divisor):  

gcf, gcd (294; 252) = 42 = 2 × 3 × 7 = 42;  

Numbers have common prime factors.

Answer 2

$<b>$ hey mate

here's your answer,

》 first of all find the prime factors of 294 as well as 252

》 294 = 2 × 3 × 7

》 252 = 2 × 2 × 3 × 3 × 7

》 cube root of 294 × 252 = 2 × 3 × 7 × 2 × 2 × 3 ×3 ×7

》 as we all know that in cube root it gets paired out in 3 number

》 cube root of 294 × 252 = 2 × 3 × 7 = 42 .

$\huge\boxed{42}$

hope it helps you mate ✔✔

be brainly ✔✔