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The largest number which divides 972 and 2016 leaving remainder 15 in each case, is
By BYJU'S Exam Prep
Updated on: September 25th, 2023
The largest number which divides 972 and 2016 while leaving 15 as a remainder in each case is 87. To find this answer, we will subtract the numbers from the remainder provided to us. After that, we will factorize these numbers to find the HCF which will provide us with our answers. Check out the detailed solution to find the largest number which divides 972 and 2016 while leaving the remainder 15 in each case below.
Table of content
Largest Number that Divides 972 and 2016 Leaving Remainder 15
To find the largest number which divides 972 and 2016 while leaving 15 as a remainder, we will first need to subtract the remainder from the original numbers. It will give us,
972 – 15 = 957
2016 – 15 = 2001
In the next step, we will find the factors of these new numbers derived after subtracting the remainder from the original numbers. This will provide us with the highest common factors of 957 and 2001 as follows:
957 = 3 × 11 × 29
2002 = 3 × 23 × 29
HCF (957, 2001)
= 3 × 29
= 87
Hence, the largest number that divides 972 and 2016 by leaving 15 as a remainder is 87.
HCF (Highest Common Factor)
HCF is also known as the Highest Common Factor, Greatest Common Divisor, and Greatest Common Measure. It refers to the greatest number that can divide each of the two or more numbers given to us. There are three types of methods by which one can find HCG, these include, the prime factorization method, the division method, and the shortcut method. It gives us a common number that can divide two or more numbers evenly.
Summary:
The largest number which divides 972 and 2016 leaving remainder 15 in each case, is
87 is the largest number that divides 972 and 2016 by leaving 15 in each case. To find this solution we found the HCF of the numbers derived after subtracting the original numbers from the remainder. After factorizing those numbers, we got the HCF 87 which is our answer.
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