About HCF Formula
The HCF formula aids in the discovery of the highest common factor between two or more numbers. The biggest number that divides all the specified numbers exactly leaving no residual is the HCF of two or more numbers. The HCF formula is similar to the LCM (least common multiple) formulae.
Meaning of HCF Formula
The HCF formula can be used to calculate the HCF of two or more numbers. The greatest common divisor of any two or more natural numbers is HCF. There are two ways for calculating a number's HCF:
Prime factorization Method: The product of the prime factors is used to express two or more numbers. HCF = Product of the lowest powers of the common prime factors.
Division Method: To determine the HCF of two numbers a and b, we utilise Euclid's Division Lemma(a = bq+ r.). Dividend = Divisor Quotient + Remainder, for example. When a divides b, q is the quotient, and r is the remainder, according to the lemma. If r is less than zero, r becomes the new divisor(b) and b the new dividend (a). Continue dividing until r equals 0. When r = 0, the HCF is b.
HCF Formulas
- The HCF of the provided numbers can be calculated using a variety of HCF formulas. Let's have a look at them:
- LCM × HCF = Product of the Numbers.If P and Q are two different numbers, then LCM (P & Q) × HCF (P & Q) = P × Q.
- Co-prime numbers' HCF is always 1. As a result, the LCM of Co-prime Numbers equals the product of the numbers.
- Division of Euclid To find the HCF of two numbers, apply the lemma. Obtain two numbers a and b such that a>b. Find a/b. Dividend = Divisor Quotient + Remainder, for example. If the remainder is zero, the divisor is the HCF; otherwise, apply the lemma to b and r and divide until the remainder is zero.
- We utilise HCF of fractions = HCF of numerators/LCM of the denominators to obtain the HCF of fractions.
- To determine the largest number that divides p, q, and r exactly. HCF of p, q, and r = required number
- To determine the largest number that divides p, q, and r, leaving a, b, and c as remainders. HCF of (p-a), (q-b), and (r-c) = required number
- HCF of any two or more numbers is never greater than any of the given numbers.
Maths Formulas prepared by HT experts are listed on the main page.
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