How to Find the Highest Common Factor (HCF) of 3/4, 5/7 and 7/16

What is the Highest Common Factor (HCF)?

The Highest Common Factor (HCF) is the largest number that is a factor of two or more numbers. It is also known as the greatest common divisor (GCD) or the greatest common factor (GCF).

Finding the HCF of 3/4, 5/7 and 7/16

The first step to finding the HCF of 3/4, 5/7 and 7/16 is to find the prime factorization of each fraction. The prime factorization of a fraction is the list of prime numbers that, when multiplied together, equal the numerator and denominator of the fraction.

For 3/4, the prime factorization of 3 is 3, and the prime factorization of 4 is 2 x 2. The HCF is the product of the common prime factors, which in this case is simply 3.

For 5/7, the prime factorization of 5 is 5, and the prime factorization of 7 is 7. In this case, the HCF is 5.

For 7/16, the prime factorization of 7 is 7, and the prime factorization of 16 is 2 x 2 x 2 x 2. The HCF is the product of the common prime factors, which in this case is 7.

The HCF of 3/4, 5/7 and 7/16 is the product of the common prime factors, which in this case is 3 x 5 x 7, or 105.

Conclusion

In conclusion, the HCF of 3/4, 5/7 and 7/16 is 105.