Question

find out the HCF of 105 135 and 120 using prime fractional method​

Answer 1

Answer:

The given integers 105 and 1515 can be factorised as follows:

105=3×5×71515=5×3×101

3,5,7 and 101 are prime numbers as these are the numbers that are only divisible by themselves. 

We know that HCF is the highest common factor, therefore, the HCF of 105 and 1515 is:

HCF=3×5=15

Also, the LCM is the least common multiple, therefore, the LCM of 105 and 1515 is:

LCM=3×5×7×101=10605

Hence, the HCF is 15 and LCM is 10605.

Answer 2

Step-by-step explanation:

Step-1: Prime Factorization of 120

Prime factors of 120 are 2, 3, 5. Prime factorization of 120 in exponential form is:

120 = 23 × 31 × 51

Step-2: Prime Factorization of 105135

Prime factors of 105135 are 3, 5, 43, 163. Prime factorization of 105135 in exponential form is:

105135 = 31 × 51 × 431 × 1631

Step-3: Factors of 120

List of positive integer factors of 120 that divides 120 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60

Step-4: Factors of 105135

List of positive integer factors of 105135 that divides 120 without a remainder.

1, 3, 5, 15, 43, 129, 163, 215, 489, 645, 815, 2445, 7009, 21027, 35045

Final Step: Greatest Common Factor Number

We found the factors and prime factorization of 120 and 105135. The biggest common factor number is the GCF number.

So the greatest common factor 120 and 105135 is 15.