The HCF of 91, 112 and 49 is 7. The highest integer which divides the numbers 91, 112 and 49 exactly is the HCF. The factors of 91 are 1, 7, 13, 91, the factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112, and the factors of 49 are 1, 7, 49. The methods to find the HCF value of the numbers are prime factorisation, long division and listing common factors.
Also read: Highest common factor
What is the HCF of 91, 112 and 49?
The answer to this question is 7. The HCF of 91, 112 and 49, using the different methods, is given in this article for your reference. The HCF of 91, 112 and 49 is 7, as it divides 91, 112 and 49 exactly.
How to Find HCF of 91, 112 and 49?
There are three methods to find the HCF of 91, 112 and 49
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 91, 112 and 49 by Prime Factorisation Method
The prime factorisation of 91, 112 and 49 is given by:
91 = 7 × 13
112 = 2 × 2 × 2 × 2 × 7
49 = 7 × 7
Common prime factors of 91, 112 and 49 = 7
Hence, HCF (91, 112, 49) = 7
HCF of 91, 112 and 49 by Long Division Method
We’ll divide (91, 112, 49) by their prime factors to determine the HCF of 91, 112 and 49 using the division method. The HCF of 91, 112 and 49 is the divisor when the remainder becomes zero in long division.
First, let us divide 91 by 49
Now again, by dividing 112 by 7
Hence, HCF (91, 112, 49) = 7
HCF of 91, 112 and 49 by Listing the Factors
Calculate the HCF of 91, 112 and 49 by listing out the common factors as shown below:
Factors of 91: 1, 7, 13, 91
Factors of 112: 1, 2, 4, 7, 8, 14, 16, 28, 56, 112
Factors of 49: 1, 7, 49
There are 2 common factors of 91, 112 and 49, and they are 1 and 7.
Therefore, the highest common factor of 91, 112 and 49 is 7.
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Video Lesson on Properties of HCF and LCM
HCF of 91, 112 and 49 Solved Example
Question: In 157, 7, 132, 126, 158, 114, 133, find the HCF of 91, 112 and 49.
Solution:
HCF of 91, 112 and 49 is the number which divides 91, 112 and 49, with the remainder as zero.
The number which satisfies this condition is 7.
Hence, the HCF is 7.
Frequently Asked Questions on HCF of 91, 112 and 49
What is the HCF of 91, 112 and 49?
Using the prime factorisation method, find the HCF of 91, 112 and 49.
What methods can be used to find HCF of 91, 112 and 49?
Find the HCF of 91, 112 and 49 using the LCM.
As per prime factorisation
91 = 7 × 13
112 = 2 × 2 × 2 × 2 × 7
49 = 7 × 7
LCM (91, 112) = 1456
LCM (112, 49) = 784
LCM (49, 91) = 637
LCM (91, 112, 49) = 10192
HCF (91, 112, 49) = [(91 × 112 × 49) x LCM (91, 112, 49)]/[LCM (91, 112) × LCM (112, 49) × LCM (49, 91)]
HCF (91, 112, 49) = (499408 × 10192)/ (1456 × 784 × 637)
HCF (91, 112, 49) = 7
Mention the relation between HCF and LCM of 91, 112 and 49.
The relation between HCF and LCM of 91, 112 and 49 is
HCF × LCM = 91 × 112 × 49
HCF × LCM = 499408
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