HCF of 3 numbers by prime factorization
Ex:
Find the H.C.F. of 324, 288 and 384.
Sol:
By resolving each of the given numbers into prime factors, we get:
H.C.F. of 324, 288 and 384
324 = 2 × 2 × 3 × 3 × 3 × 3
= 22 × 34
288 = 2 × 2 × 2 × 2 × 2 × 3 × 3
= 25 × 32
384 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3
= 27 × 3
The common factors of 324, 288 and 384 are: 2 (occurring twice) and 3 (occurring once).
∴ H.C.F. = 22 × 3
= 4 × 3
= 12