5th Grade Highest Common Factor (H.C.F.)
The highest common factor (H.C.F.) of two or more numbers is the highest or greatest common number or divisor which divides each given number exactly. Hence, it is also called Greatest Common Divisor (GCD).
We can find the H.C.F. of the given numbers using the following methods.
I. By factorization or prime factorization method
II. By short division method
III. By long division method
CASE I. Finding the H.C.F. by Prime Factorisation Method:
Solved Example:
1. Find the H.C.F. of 12, 36 and 48.
Prime factors of 12 = 2 × 2 × 3
Prime factors of 36 = 2 × 2 × 3 × 3
Prime factors of 48 = 2 × 2 × 2 × 2 × 3
The highest common factor is 12 (2 × 2 × 3) which is common in all given numbers.
So, the H.C.F. of the given numbers = 2 × 2 × 3 = 12
Factorisation Method
We can use the simple factorisation method also for finding the H.C.F. of the given numbers.
Factors of 12 are 1, 2, 3, 4, 6, 12.
Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.
Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
We see that 12 is the greatest common factor.
So, the H.C.F. of the given numbers = 12
CASE II. Finding the H.C.F. by Short Division Method:
Solved Example:
1. Find the H.C.F. of 12, 36, 48.
Solution:
Step I: Divide the numbers by the smallest common prime factor
Step II: Divide again by the smallest or the next smallest common prime factor
Step III: Stop as there is no common prime factor of 1, 2, 4.
The H.C.F. of 12, 36 and 48 is the product of the common prime factors i.e. 2 × 2 × 3 = 12.
CASE III. Finding the H.C.F. by Long Division Method:
In this method, we divide greater number by smaller number. The remainder is treated as the divisor and the divisor as the dividend for the next step. We proceed in this manner till the remainder is 0. The last divisor is the H.C.F. of the given numbers.
Solved Example:
1. Find the H.C.F. of 300 and 888.
Solution:
STEPS
(i) Divide the bigger number 888 by the smaller number 300
(ii) Now, the remainder 288 becomes the divisor and the divisor 300 becomes the dividend
(iii) Treat the remainder 12 as the divisor and divisor 288 as the dividend.
So, the H.C.F. of 300 and 888 is 12.
Sometimes, we are asked to find the H.C.F. of more than two numbers such as three numbers. In such cases, we generally find the H.C.F. of the largest and the second largest numbers. Then we find the H.C.F. of the smallest number and the number found as the H.C.F. of two larger numbers. The last divisor is the H.C.F. of the given numbers.
2. Find the H.C.F. of 650, 900 and 1000
Solution:
First we find the H.C.F. of greater numbers i.e. 1000 and 900.
So, the H.C.F of 900 and 1000 is 100.
Now we find the H.C.F. of 100 and the smallest given number i.e., 650.
So, the H.C.F. of 100 and 650 is 50.
Hence, the H.C.F. of 650, 900 and 1000 is 50.
5th Grade Highest Common Factor Worksheet
I. Find the H.C.F. of the following numbers by factorisation method:
1. 28 and 35
2. 64 and 72
3. 36 and 81
4. 45 and 105
5. 45, 60 and 75
6. 20, 30 and 40
7. 28, 35 and 42
8. 20, 30 and 60
9. 36, 40 and 50
10. 25, 100 and 150
11, 12, 48 and 296
12. 40, 290 and 380
13. 20, 120 and 240
14. 28, 180 and 280
15. 120, 240 and 620
16. 142, 284 and 426
Answer:
I. 1. 7
2. 8
3. 9
4. 15
5. 15
6. 10
7. 7
8. 10
9. 2
10. 25
11. 4
12. 10
13. 20
14. 4
15. 20
16. 142
II. Find the H.C.F. of the following numbers by prime factorisation method:
1. 80 and 144
2. 78 and 104
3. 92 and 138
4. 80 and 125
5. 64, 128 and 256
6. 144, 256 and 224
7. 198, 360 and 930
8. 40, 90 and 125
9. 80, 120 and 160
10. 50, 250 and 300
11. 40, 390, and 400
12. 63, 315 and 441
14. 120, 250 and 380
13. 70, 280 and 420
15. 70, 210 and 570
16. 76, 360 and 1260
Answer:
II. 1. 16
2. 26
3. 46
4. 5
5. 64
6. 16
7. 6
8. 5
9. 40
10. 50
11. 10
12. 63
13. 70
14. 10
15. 10
16. 4
III. Find the H.C.F. of the following numbers by short division method.
1. 40, 80 and 120
3. 35, 70 and 112
5. 56, 252 and 504
7. 24,120 and 720
9. 120, 260 and 480
11. 90, 495 and 990
13. 40, 90 and 440
15. 45, 125 and 260
2. 26, 52 and 65
4. 16, 24 and 32
6. 55, 250 and 500
8. 150,120 and 360
10. 25, 60 and 225
12. 80, 140 and 240
14. 35, 95 and 225
16. 110, 230 and 360
Answer:
III. 1. 40
2. 13
3. 7
4. 8
5. 28
6. 5
7. 24
8. 30
9. 20
10. 5
11. 45
12. 20
13. 10
14. 5
15. 5
16. 10
IV. Find the H.C.F. of following numbers by long division method:
1. 80 and 176
2. 864 and 945
3. 272, 544 and 816
4. 690, 960 and 1150
5. 360, 675 and 720
6. 1350, 1530 and 1650
7. 220, 830 and 1660
8. 620,1240 and 1860
9. 140, 240 and 340
10. 80, 120 and 440
11. 120, 210, and 300
12. 25, 95 and 195
13. 135, 275 and 300
14. 75, 150 and 325
15. 200, 320 and 490
16. 124, 372 and 496
Answer:
IV. 1. 16
2. 27
3. 272
4. 10
5. 45
6. 30
7. 10
8. 620
9. 20
10. 40
11. 30
12. 5
13. 5
14. 25
15. 10
16. 124
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