What is gcd 270,360 ?

The solution to gcd 270,360 is 90

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Find the GCF 270 , 360

gcf

270, 360

90

Solution steps

270, 360

Prime factorization of

270 : 2 \cdot 3 \cdot 3 \cdot 3 \cdot 5

270

270

divides by

2270 = 135 \cdot 2

= 2 \cdot 135

135

divides by

3135 = 45 \cdot 3

= 2 \cdot 3 \cdot 45

45

divides by

345 = 15 \cdot 3

= 2 \cdot 3 \cdot 3 \cdot 15

15

divides by

315 = 5 \cdot 3

= 2 \cdot 3 \cdot 3 \cdot 3 \cdot 5

2, 3, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3 \cdot 3 \cdot 3 \cdot 5

Prime factorization of

360 : 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5

360

360

divides by

2360 = 180 \cdot 2

= 2 \cdot 180

180

divides by

2180 = 90 \cdot 2

= 2 \cdot 2 \cdot 90

90

divides by

290 = 45 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 45

45

divides by

345 = 15 \cdot 3

= 2 \cdot 2 \cdot 2 \cdot 3 \cdot 15

15

divides by

315 = 5 \cdot 3

= 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5

2, 3, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5

The prime factors common to

270, 360

are

= 2 \cdot 3 \cdot 3 \cdot 5

Multiply the numbers:

2 \cdot 3 \cdot 3 \cdot 5 = 90

= 90

t o a p erce n t a g e 9/60

\frac{71}{3}

t h e \frac{63}{36}

t h e \frac{98}{49}

ro u n d t o t h e n e a res t t e n t h 8.06