Prime factors of 36 are: 2^2 and 3^2
Prime factors of 144 are: 2^4 and 3^2
Prime factors common to both number are 2^2 and 3^2 which when multiplied equals 36 making it the HCF
144 = 2^4*3^236 = 2^2*3^2
HCF = lowest powers of each prime between the two factorisations.
So HCF = 2^2*3^2 = 36.
ladder method of 144
24 x 32 = 144
The GCF of 84 and 144 is 12. You must do the prime factorization of each number. The prime factorization of 144 is 2 to the fourth power times 3 squared. The prime factorization of 84 is 2 squared times 7 times 3. You take the least of each common factor which would be 2 squared and 3. Two squared equals 4 and 4 times 3 equals 12, so the GCF is 12.
The prime factorizations are: 60: 2 X 2 X 3 X 5 120: 2 X 2 X 2 X 3 X 5 144: 2 x 2 x 2 X 2 X 3 X 3
144 72,2 36,2,2 18,2,2,2 9,2,2,2,2 3,3,2,2,2,2
ladder method of 144
Since 72 is a factor of 144, its whole prime factorization will be contained in the prime factorization of 144.
Since 72 is a factor of 144, its entire prime factorization will be contained in the prime factorization of 144.
2 * 2 * 2 * 2 * 3 * 3 = 144
It is: 2*2*2*2*3*3 = 144 or in exponents 24*32 = 144
144 72,2 36,2,2 18,2,2,2 9,2,2,2,2 3,3,2,2,2,2
2x2x2x2x3x3
since 144 is 122 you can find the primefactorization easy by noting that 12=22 x3 so 144=24x32
144 = 24 32
The prime factors of 144 are: 2,3
24*32 = 144
144 = 24 x 32