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What is the HCF of 3/5, 7/10, 2/15, 6/21?
- a)5/123
- b)6/121
- c)2/105
- d)1/210
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
What is the HCF of 3/5, 7/10, 2/15, 6/21?a)5/123b)6/121c)2/105d)1/210e...
HCF will be HCF of numerators/LCM of denominators
So HCF = HCF of 3,7,2,6)/(LCM of 5,10, 15, 21)
= 1/210
So HCF = HCF of 3,7,2,6)/(LCM of 5,10, 15, 21)
= 1/210
Most Upvoted Answer
What is the HCF of 3/5, 7/10, 2/15, 6/21?a)5/123b)6/121c)2/105d)1/210e...
To find the Highest Common Factor (HCF) of fractions, we need to find the HCF of their numerators and denominators separately.
Step 1: Finding the HCF of the Numerators
The numerators of the given fractions are 3, 7, 2, and 6. To find their HCF, we can use the Euclidean algorithm or prime factorization method.
Using the prime factorization method:
- The prime factors of 3 are: 3
- The prime factors of 7 are: 7
- The prime factors of 2 are: 2
- The prime factors of 6 are: 2, 3
The common prime factors among all the numerators are 2 and 3. So, the HCF of the numerators is 2 * 3 = 6.
Step 2: Finding the HCF of the Denominators
The denominators of the given fractions are 5, 10, 15, and 21. Similarly, we can find their HCF.
Using the prime factorization method:
- The prime factors of 5 are: 5
- The prime factors of 10 are: 2, 5
- The prime factors of 15 are: 3, 5
- The prime factors of 21 are: 3, 7
The common prime factors among all the denominators are 5. So, the HCF of the denominators is 5.
Step 3: Simplifying the Result
Now that we have found the HCF of the numerators and denominators separately, we can express the HCF of the fractions as the simplified fraction.
The HCF of the given fractions is 6/5.
Therefore, the correct answer is option D) 1/210.
Step 1: Finding the HCF of the Numerators
The numerators of the given fractions are 3, 7, 2, and 6. To find their HCF, we can use the Euclidean algorithm or prime factorization method.
Using the prime factorization method:
- The prime factors of 3 are: 3
- The prime factors of 7 are: 7
- The prime factors of 2 are: 2
- The prime factors of 6 are: 2, 3
The common prime factors among all the numerators are 2 and 3. So, the HCF of the numerators is 2 * 3 = 6.
Step 2: Finding the HCF of the Denominators
The denominators of the given fractions are 5, 10, 15, and 21. Similarly, we can find their HCF.
Using the prime factorization method:
- The prime factors of 5 are: 5
- The prime factors of 10 are: 2, 5
- The prime factors of 15 are: 3, 5
- The prime factors of 21 are: 3, 7
The common prime factors among all the denominators are 5. So, the HCF of the denominators is 5.
Step 3: Simplifying the Result
Now that we have found the HCF of the numerators and denominators separately, we can express the HCF of the fractions as the simplified fraction.
The HCF of the given fractions is 6/5.
Therefore, the correct answer is option D) 1/210.
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