Question

HCF using the prime factorisation method 70,105,245​

Answer 1

We are given the numbers 70, 105 and 175

Now, we will find the factors of all the numbers using the method of prime factorization

First, we will find the factors of 70 using prime factorization.

Now as 70 is an even number, so we will divide it by the least prime number 2. Therefore, we get

70÷2=35

Here, we cannot divide 35 by 3 as 3 is not a factor of 35.

Now dividing the 35 by next least prime number 5, we get

35÷5=7

Now as we have obtained our quotient as prime number, we will not factorize it further.

Thus, the factors of 70 are 2, 5 and 7 and can be written as:

70=2×5×7

We will now find the factors of 105 using prime factorization, we get

Now as 105 is an odd number, so we will divide it by least odd prime number 3.

105÷3=35

Now dividing the 35 by next least prime number 5, we get

35÷5=7

Now as we have obtained our quotient as prime number, we will not factorize it further.

Thus, the factors of 150 are 3, 5 and 7 and can be written as:

105=3×5×7

Now, we will find the factors of 175 using prime factorization.

Now as 175 is an odd number, so we will divide it by least prime number 5.

175÷5=35

Now dividing the 35 by 5, we get

35÷5=7

Now as we have obtained our quotient as prime number, we will not factorize it further.

Thus, the factors of 175 are 5, 5 and 7 and can be written as:

175=5×5×7

Thus the factors of all the numbers are represented with the same bases as:

70=21×30×51×71105=20×31×51×71175=20×30×52×71

Now, we will find the HCF for the given numbers from the factors.

Highest common factor is a factor which is common for all the factors.

Thus, we get

HCF(70,105,175)=20×30×51×71

Applying the exponent, we get

⇒HCF(70,105,175)=1×1×5×7

Multiplying the terms, we get

⇒HCF(70,105,175)=35

Therefore, the HCF of 70, 105 and 175 is 35.

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