Join 60,000+ competitive exam aspirants
or with email
Your Cart
SubtotalтВ╣0
TotalтВ╣0
Examoogle тАв User тАв info@examoogle.com тАв EE-2024-8821
Chapter 1 of 12 тАв Page 1 of 248ЁЯФТ Protected PDF тАв Watermarked
Join 60,000+ competitive exam aspirants
The HCF of 45, 78 and 117 is:
9
7
3
5
3
Check the options starting from the largest value. Since 3 is the only factor in the provided images (9, 7, 3, 5) that divides 45, 78, and 117, it must be the answer.
The numbers to find the Highest Common Factor (HCF) for are 45, 78, and 117.
HCF(a,b,c)=Greatest┬аcommon┬аdivisor┬аof┬аa,b,c
Check the options starting from the largest value. Since 3 is the only factor in the provided images (9, 7, 3, 5) that divides 45, 78, and 117, it must be the answer.
Students often stop after finding a common factor of 3 and mistake 9 for the HCF, but 78 is not divisible by 9.
Prime factorization of the numbers
Perform prime factorization for each number: 45=32├Ч5, 78=2├Ч3├Ч13, and 117=32├Ч13.
45=3├Ч3├Ч5,78=2├Ч3├Ч13,117=3├Ч3├Ч13
Identify common prime factors
The only prime factor common to all three numbers is 3. We take the smallest exponent of the common prime factor, which is 31.
HCF=31=3
C is correct because the prime factorization shows that 3 is the greatest common divisor of 45, 78, and 117.
HCF and LCM are fundamental in number systems; always look for the smallest prime factor when dealing with large numbers to simplify calculations quickly.
Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.
Free Download тАв 100K+ Aspirants