HCF of 12 and 18 is the largest possible number that divides 12 and 18 exactly without any remainder. The factors of 12 and 18 are 1, 2, 3, 4, 6, 12 and 1, 2, 3, 6, 9, 18 respectively. There are 3 commonly used methods to find the HCF of 12 and 18 - long division, Euclidean algorithm, and prime factorization. Show
What is HCF of 12 and 18?Answer: HCF of 12 and 18 is 6.  Explanation: The HCF of two non-zero integers, x(12) and y(18), is the highest positive integer m(6) that divides both x(12) and y(18) without any remainder. Methods to Find HCF of 12 and 18Let's look at the different methods for finding the HCF of 12 and 18.
HCF of 12 and 18 by Prime FactorizationPrime factorization of 12 and 18 is (2 × 2 × 3) and (2 × 3 × 3) respectively. As visible, 12 and 18 have common prime factors. Hence, the HCF of 12 and 18 is 2 × 3 = 6. HCF of 12 and 18 by Long DivisionHCF of 12 and 18 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
The corresponding divisor (6) is the HCF of 12 and 18. HCF of 12 and 18 by Listing Common Factors
There are 4 common factors of 12 and 18, that are 1, 2, 3, and 6. Therefore, the highest common factor of 12 and 18 is 6. ☛ Also Check:
HCF of 12 and 18 Examples
Example 2: Find the highest number that divides 12 and 18 exactly. Solution: The highest number that divides 12 and 18 exactly is their highest common factor, i.e. HCF of 12 and 18.
Therefore, the HCF of 12 and 18 is 6.
Example 3: Find the HCF of 12 and 18, if their LCM is 36. Solution: ∵ LCM × HCF = 12 × 18 ⇒ HCF(12, 18) = (12 × 18)/36 = 6 Therefore, the highest common factor of 12 and 18 is 6. go to slidego to slidego to slide
The HCF of 12 and 18 is 6. To calculate the Highest common factor of 12 and 18, we need to factor each number (factors of 12 = 1, 2, 3, 4, 6, 12; factors of 18 = 1, 2, 3, 6, 9, 18) and choose the highest factor that exactly divides both 12 and 18, i.e., 6. What is the Relation Between LCM and HCF of 12, 18?The following equation can be used to express the relation between Least Common Multiple and HCF of 12 and 18, i.e. HCF × LCM = 12 × 18. What are the Methods to Find HCF of 12 and 18?There are three commonly used methods to find the HCF of 12 and 18.
If the HCF of 18 and 12 is 6, Find its LCM.HCF(18, 12) × LCM(18, 12) = 18 × 12 Since the HCF of 18 and 12 = 6 ⇒ 6 × LCM(18, 12) = 216 Therefore, LCM = 36 ☛ HCF Calculator How to Find the HCF of 12 and 18 by Long Division Method?To find the HCF of 12, 18 using long division method, 18 is divided by 12. The corresponding divisor (6) when remainder equals 0 is taken as HCF. How to Find the HCF of 12 and 18 by Prime Factorization?To find the HCF of 12 and 18, we will find the prime factorization of the given numbers, i.e. 12 = 2 × 2 × 3; 18 = 2 × 3 × 3. ⇒ Since 2, 3 are common terms in the prime factorization of 12 and 18. Hence, HCF(12, 18) = 2 × 3 = 6 ☛ Prime Number
We will learn the relationship between H.C.F. and L.C.M. of
two numbers. First we need to find the highest common factor (H.C.F.) of 15 and 18 which is 3. Then we need to find the lowest common multiple (L.C.M.) of 15 and 18 which is 90. H.C.F. × L.C.M. = 3 × 90 = 270 Also the product of numbers = 15 × 18 = 270 Therefore, product of H.C.F. and L.C.M. of 15 and 18 = product of 15 and 18. Again, let us consider the two numbers 16 and 24 Prime factors of 16 and 24 are: 16 = 2 × 2 × 2 × 2 24 = 2 × 2 × 2 × 3 L.C.M. of 16 and 24 is 48; H.C.F. of 16 and 24 is 8; L.C.M. × H.C.F. = 48 × 8 = 384 Product of numbers = 16 × 24 = 384 So, from the above explanations we conclude that the product of highest common factor (H.C.F.) and lowest common multiple (L.C.M.) of two numbers is equal to the product of two numbers or, H.C.F. × L.C.M. = First number × Second number or, L.C.M. = \(\frac{\textrm{First Number} \times \textrm{Second Number}}{\textrm{H.C.F.}}\) or, L.C.M. × H.C.F. = Product of two given numbers or, L.C.M. = \(\frac{\textrm{Product of Two Given Numbers}}{\textrm{H.C.F.}}\) or, H.C.F. = \(\frac{\textrm{Product of Two Given Numbers}}{\textrm{L.C.M.}}\) Solved examples on the
relationship between H.C.F. and L.C.M.: 1. Find the L.C.M. of 1683 and 1584. Solution: First we find highest common factor of 1683 and 1584 Therefore, highest common factor of 1683 and 1584 = 99 Lowest common multiple of 1683 and 1584 = First number × Second number/ H.C.F. = \(\frac{1584 × 1683}{99}\) = 26928 2. Highest common factor and lowest common multiple of two numbers are 18 and 1782 respectively. One number is 162, find the other. Solution: We know, H.C.F. × L.C.M. = First number × Second number then we get, 18 × 1782 = 162 × Second number \(\frac{18 × 1782}{162}\) = Second number Therefore, the second number = 198 3. The HCF of two numbers is 3 and their LCM is 54. If one of the numbers is 27, find the other number. Solution: HCF × LCM = Product of two numbers 3 × 54 = 27 × second number Second number = \(\frac{3 × 54}{27}\) Second number = 6 4. The highest common factor and the lowest common multiple of two numbers are 825 and 25 respectively. If one of the two numbers is 275, find the other number. Solution: We know, H.C.F. × L.C.M. = First number × Second number then we get, 825 × 25 = 275 × Second number \(\frac{825 × 25}{275}\) = Second number Therefore, the second number = 75 5. Find the H.C.F. and L.C.M. of 36 and 48. Solution:
Therefore, product of the two numbers = H.C.F × L.C.M. 2. The H.C.F. of two numbers 30 and 42 is 6. Find the L.C.M. Solution: We have H.C.F. × L.C.M. = product of the numbers 6 × L.C.M. = 30 × 42 L.C.M. = \[\frac{30 × 42}{\sqrt{6}}\] = \[\frac{1260}{\sqrt{6}}\] = 210 3. Find the greatest number which divides 105 and 180 completely. Solution:
Therefore, the greatest number that divides 105 and 180 completely is 15. 4. Find the least number which leaves 3 as remainder when divided by 24 and 42. Solution:
The least number which leaves 3 as remainder is 168 + 3 = 171. Important Notes: Two numbers which have only 1 as the common factor are called co-prime. The least common multiple (L.C.M.) of two or more numbers is the smallest number which is divisible by all the numbers. If two numbers are co-prime, their L.C.M. is the product of the numbers. If one number is the multiple of the other, then the multiple is their L.C.M. L.C.M. of two or more numbers cannot be less than any one of the given numbers. H.C.F. of two or more numbers is the highest number that can divide the numbers without leaving any remainder. If one number is a factor of the second number then the smaller number is the H.C.F. of the two given numbers. The product of L.C.M. and H.C.F. of two numbers is equal to the product of the two given numbers. Questions and Answers on Relationship between H.C.F. and L.C.M. 1. The H.C.F. of two numbers 20 and 75 is 5. Find their L.C.M. 2. The L.C.M. of two numbers 72 and 180 is 360. Find their H.C.F. 3. The L.C.M. of two numbers is 120. If the product of the numbers is 1440, find the H.C.F. 4. Find the least number which leaves 5 as remainder when divided by 36 and 54. 5. The product of two numbers is 384. If their H.C.F. is 8, find the L.C.M. Answer: 1. 300 2. 36 3. 12 4. 113 5. 48
Common Multiples. Least Common Multiple (L.C.M). To find Least Common Multiple by using Prime Factorization Method. Examples to find Least Common Multiple by using Prime Factorization Method. To Find Lowest Common Multiple by using Division Method Examples to find Least Common Multiple of two numbers by using Division Method Examples to find Least Common Multiple of three numbers by using Division Method Relationship between H.C.F. and L.C.M. Worksheet on H.C.F. and L.C.M. Word problems on H.C.F. and L.C.M. Worksheet on word problems on H.C.F. and L.C.M. 5th Grade Math Problems From Relationship between H.C.F. and L.C.M. to HOME PAGE
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HCF of two numbers is 18 if the numbers are in the ratio 5 is to 7
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