if hcf of 144 and 180 is expressed in the form 13m-3
If hcf of 144 and 180 is expressed in the form 13m-3
Answer:
To find the highest common factor (HCF) of 144 and 180, we need to first prime factorize both numbers.
Prime Factorization of 144:
144 = 2^4 \times 3^2
Prime Factorization of 180:
180 = 2^2 \times 3^2 \times 5
To find the HCF, we take the minimum power of each prime factor that appears in both numbers.
Therefore, the HCF of 144 and 180 is 2^2 \times 3^2 = 36.
Now, we are asked to express this HCF in the form of 13m-3.
Since 36 = 13 \times 3 - 3, we can write 36 as 13m-3 where m = 3.
So, the HCF of 144 and 180, expressed in the form of 13m-3, is 13(3) - 3 = 36.