Highest Common Factor (HCF)

Find the greatest weight in $\mathrm{kg}$ that can be used a number of times to weigh $156 \mathrm{kg}, 180 \mathrm{kg}, 324 \mathrm{kg}$ of wheat.

Find the greatest length in $\mathrm{cm}$ of a tape whose length can be used to measure exactly the lengths $56 \mathrm{cm}, 154 \mathrm{cm}, 294 \mathrm{cm}$.

Reduce the following fraction to the lowest term.

$\frac{350}{518}$

Reduce the following fraction to the lowest term.

$\frac{611}{1457}$

Reduce the following fraction to the lowest term.

$\frac{559}{989}$

Reduce the following fraction to the lowest term.

$\frac{306}{414}$

In a school library, there are $780$ books of English, $364$ books of Hindi and $624$ books of mathematics. The librarian wants to arrange these books across the maximum number of shelves such that each shelf has the same number of books of each subject. Find the number of shelves that can be used. What would be the number of these books in each shelf?

There are $342$ apples, $627$ mangoes, $836$ guavas. These are to be arranged in heaps containing the same number of fruits. Find the greatest number of fruits possible in each heap. How many heaps are formed?

Use HCF to prove that the following numbers are coprimes.

$1365$ and $2057$.

Use HCF to prove that the following numbers are co-primes.

$980$ and $1287$.

Find the greatest number that will divide $37, 56, 93$ leaving remainder $1, 2, 3$.

What is the greatest number that will divide $139$,$184$ and $424$, leaving the remainder $4$ in each case?

What is the greatest number that will divide $33$ and $45$ leaving $9$ as remainder in each case?

What is the largest number that has the multiples$168$ and $288$.

Find the largest number that divides $540, 315, 360$.

Find the greatest number that will divide $58$ and $145$ exactly.

Find the HCF of $84, 56, 35, 112$

Find the HCF of $60, 84, 108, 132$.

Find the HCF of $1326, 3094, 4420$.

Find the HCF of $176, 1100, 4444$.