HCF Question and Answers

Questions​ and Answers for HCF

Highest Common Factor (HCF) of two or more numbers is the greatest number that can divide each number evenly or accurately.On this page you’ll find HCF Question and Answers to practice and improve your concept and understanding of HCF.

HCF and LCM Questions and Answers

Formulas or Rules for finding HCF Question and Answers

HCF in case of only two numbers:

  • Suppose the question asks to calculate the HCF of any two numbers. Then Divide the greater number by the smaller one.
  • Now divide the divisor by the remainder.
  • Keep dividing the preceding divisor with the remainder until a Zero remainder is obtained.
  • The last divisor obtained will be the HCF of those two given numbers.

HCF Question and Answers In case of more than two numbers :

  • Choose any two numbers and find their HCF by applying the method mentioned above.
  • The HCF of these two numbers and the third number will be the HCF of all three numbers and so forth.

Types of HCF

There are various methods that are used to find the Highest Common Factor (HCF) and Least Common Multiple (LCM) of numbers. The most common methods that are used to find HCF are :

  • Prime factorization method
  • Division method

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HCF Questions and Answers 

1. Find the HCF of 777 and 1147?

13

13

12%

55

55

5.43%

24

24

3.71%

37

37

78.86%

Therefore HCF of 777 and 1147 is 37

2. What is the HCF of 6851, 9061, 18462?

15

15

4.11%

17

17

77.74%

20

20

7.53%

33

33

10.62%

it will show some wrong but explanation is correct

Firstly let's consider any two numbers

Therefore HCF of 6891 and 9061 is 221.

Now consider 221 and the third number 18462. So its HCF is :

221   18462  83

Hence HCF of 221 and 18462 is 17.

3. What is the HCF of 598, 874?

49

49

6.95%

47

47

6.95%

46

46

76.49%

None of the above

None of the above

9.6%

it will show some wrong but explanation is correct

Therefore HCF of 598 and 874 is 46

4. what is the HCF of 32712, 4002?

174

174

81.05%

175

175

7.26%

179

179

4.84%

181

181

6.85%

32712=4002*8+696

4002=696*5+522

696=522*1+174

522=174*3+0

HCF=174Ans.

5. What is the HCF of 2923, 3239?

74

74

7.56%

75

75

5.04%

79

79

80.25%

81

81

7.14%

it will show some wrong but explanation is correct

2923 ) 3239 ( 1

-  2923

316 ) 2923 ( 9

-  2844

79 ) 316 ( 4

- 316

X

HCF is 79Ans.

6. what is the HCF of 42, 63 & 140?

7

7

87.79%

5

5

6.87%

9

9

2.29%

8

8

3.05%

42 factors are 2 x 3 x 7

63 factors are 3 x 3 x 7

140 factors are 2 x 7 x 2 x 5

SoHCF is 7Ans

7. Find the HCF of 3/8, 5/12, and 9/14?

HCF 1/168

HCF 1/168

77.21%

HCF 2/169

HCF 2/169

5.51%

HCF 5/168

HCF 5/168

9.56%

None of the Above

None of the Above

7.72%

: HCF = HCF of 3, 5, and 9

LCM of 8, 12, 14

LCM of 8, 12, 14=

2 8, 12, 14
2 4, 6, 7
2 2, 3, 7
3 1, 3, 7
7 1, 1, 7
1, 1, 1

 =  1

2*2*2*3*7

  =1/168

8. Find the highest number, which divides 590   908   1014 and leaves the same remainder in each case?

150

150

10.36%

106

106

72.51%

159

159

9.16%

57

57

7.97%

Since the required number that divides 590   908   1014, leaves the same remainder in each case, which means that number will accurately divide the difference of any two numbers.

So Consequently the required number = HCF (908 - 590), (1014 - 908) and (1014 - 590), In other words it will be the HCF of 318  ,106,   424

318= 2 x 3 x 53

106= 2 x 53

424= 2 x 2 x 2 x 53

HCf is 2 x 53

=106 Ans.

Hence the required number = 106

9. The HCF of two number is 42, and their LCM is 1260. If one of the figures is 210, find the other number?

250

250

5.17%

252

252

87.08%

256

256

4.43%

248

248

3.32%

The basic theorem is

The product of two numbers = The outcome of their HCF and LCM

Their LCM= Product of the numbers

HCF of the numbers

Therefore the other number = 42*1260/210= 252

Hence option B is the correct one.

10. Calculate the HCF of 22 and 33

11

11

94.58%

12

12

2.03%

15

15

1.69%

None of the above

None of the above

1.69%

22 = 2*11

33 = 3*11

So the HCF will be 11

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