Advertisements
Advertisements
Question
The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is ______.
Options
13
65
875
1750
Advertisements
Solution
The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is 13.
Explanation:
We have to find the largest number which divides 70 and 125
Leaving remainders 5 and 8
This can be also written as,
To find the largest number which exactly divides (70 – 5) and (125 – 8)
The largest number that divides 65 and 117 is also the Highest Common Factor of 65 and 117
Therefore, the required number is the HCF of 65 and 117
Factors of 65 = 1, 5, 13, 65
Factors of 117 = 1, 3, 9, 13, 39, 117
Common Factors = 1, 13
Highest Common factor (HCF) = 13
i.e., The largest number which divides 70 and 125
Leaving remainders 5 and 8, respectively = 13
APPEARS IN
RELATED QUESTIONS
Find the LCM and HCF of the following integers by applying the prime factorisation method.
12, 15 and 21
Given that HCF (306, 657) = 9, find LCM (306, 657).
There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?
A merchant has 120 liters of oil of one kind, 180 liters of another kind and 240 liters of third kind. He wants to sell the oil by filling the three kinds of oil in tins of equal capacity. What should be the greatest capacity of such a tin?
Determine the prime factorisation of the following positive integer:
20570
Determine the prime factorisation of the following positive integer:
58500
Write down the decimal expansions of the following rational numbers by writing their denominators in the form 2m × 5n, where m, n are non-negative integers.
\[\frac{13}{125}\]
If the prime factorization of a natural number n is 23 × 32 × 52 × 7, write the number of consecutive zeros in n.
Express the number as a product of its prime factor:
156
Find the LCM and HCF of the following pair of integers and verify that LCM × HCF = product of the two numbers.
336 and 54
If m, n are natural numbers, for what values of m, does 2n × 5m ends in 5?
What is the smallest number that when divided by three numbers such as 35, 56 and 91 leaves remainder 7 in each case?
The ratio of LCM and HCF of the least composite and the least prime numbers is ______.
Explain why 3 × 5 × 7 + 7 is a composite number.
If two positive integers p and q can be expressed as p = ab2 and q = a3b; a, b being prime numbers, then LCM (p, q) is ______.
Can two numbers have 18 as their HCF and 380 as their LCM? Give reasons.
Find the HCF and LCM of 72 and 120.
Assertion (A): The HCF of two numbers is 5 and their product is 150. Then their LCM is 40.
Reason(R): For any two positive integers a and b, HCF (a, b) × LCM (a, b) = a × b.
(HCF × LCM) for the numbers 30 and 70 is ______.
The HCF of the smallest 2-digit number and the smallest composite number is ______.
