Class 5 HCF

HCF Practice Problems

Highest Common Factor (HCF) using Prime Factorization and Long Division Methods

Find the Highest Common Factor (HCF) of the following numbers using the specified method.

Problem	Method	Solution Steps	Answer
1a. 50 and 75	Prime Factorization	50 = 2 × 5² 75 = 3 × 5² HCF = 5² = 25	25
1b. 245 and 375	Prime Factorization	245 = 5 × 7² 375 = 3 × 5³ HCF = 5	5
1c. 225 and 625	Prime Factorization	225 = 3² × 5² 625 = 5⁴ HCF = 5² = 25	25
1d. 18, 54, 72	Prime Factorization	18 = 2 × 3² 54 = 2 × 3³ 72 = 2³ × 3² HCF = 2 × 3² = 18	18
1e. 65, 90, 105	Prime Factorization	65 = 5 × 13 90 = 2 × 3² × 5 105 = 3 × 5 × 7 HCF = 5	5
1f. 72, 99, 108	Prime Factorization	72 = 2³ × 3² 99 = 3² × 11 108 = 2² × 3³ HCF = 3² = 9	9
1g. 96, 144, 168	Prime Factorization	96 = 2⁵ × 3 144 = 2⁴ × 3² 168 = 2³ × 3 × 7 HCF = 2³ × 3 = 24	24
1h. 80, 110, 210	Prime Factorization	80 = 2⁴ × 5 110 = 2 × 5 × 11 210 = 2 × 3 × 5 × 7 HCF = 2 × 5 = 10	10
1i. 675, 275, 325	Prime Factorization	675 = 3³ × 5² 275 = 5² × 11 325 = 5² × 13 HCF = 5² = 25	25
1j. 117, 65 and 78	Prime Factorization	117 = 3² × 13 65 = 5 × 13 78 = 2 × 3 × 13 HCF = 13	13
2a. 105, 252	Long Division	252 ÷ 105 = 2 rem 42 105 ÷ 42 = 2 rem 21 42 ÷ 21 = 2 rem 0 HCF = 21	21
2b. 540, 360	Long Division	540 ÷ 360 = 1 rem 180 360 ÷ 180 = 2 rem 0 HCF = 180	180
2c. 987, 462	Long Division	987 ÷ 462 = 2 rem 63 462 ÷ 63 = 7 rem 21 63 ÷ 21 = 3 rem 0 HCF = 21	21
2d. 924, 1320	Long Division	1320 ÷ 924 = 1 rem 396 924 ÷ 396 = 2 rem 132 396 ÷ 132 = 3 rem 0 HCF = 132	132
2e. 1440, 960	Long Division	1440 ÷ 960 = 1 rem 480 960 ÷ 480 = 2 rem 0 HCF = 480	480
2f. 1190, 1540	Long Division	1540 ÷ 1190 = 1 rem 350 1190 ÷ 350 = 3 rem 140 350 ÷ 140 = 2 rem 70 140 ÷ 70 = 2 rem 0 HCF = 70	70
2g. 1980, 1350	Long Division	1980 ÷ 1350 = 1 rem 630 1350 ÷ 630 = 2 rem 90 630 ÷ 90 = 7 rem 0 HCF = 90	90
2h. 252, 375, 420	Long Division	First find HCF of 252 and 375: 375 ÷ 252 = 1 rem 123 252 ÷ 123 = 2 rem 6 123 ÷ 6 = 20 rem 3 6 ÷ 3 = 2 rem 0 → HCF = 3 Now find HCF of 3 and 420: 420 ÷ 3 = 140 rem 0 HCF = 3	3
2i. 144, 252, 360	Long Division	First find HCF of 144 and 252: 252 ÷ 144 = 1 rem 108 144 ÷ 108 = 1 rem 36 108 ÷ 36 = 3 rem 0 → HCF = 36 Now find HCF of 36 and 360: 360 ÷ 36 = 10 rem 0 HCF = 36	36
2j. 2520, 3360, 4680	Long Division	First find HCF of 2520 and 3360: 3360 ÷ 2520 = 1 rem 840 2520 ÷ 840 = 3 rem 0 → HCF = 840 Now find HCF of 840 and 4680: 4680 ÷ 840 = 5 rem 480 840 ÷ 480 = 1 rem 360 480 ÷ 360 = 1 rem 120 360 ÷ 120 = 3 rem 0 HCF = 120	120

HCF Calculation Tips

Prime Factorization Method: Find common prime factors with the smallest exponents
Long Division Method: Divide larger number by smaller, then divide divisor by remainder, repeat until remainder is 0
For three numbers, find HCF of two numbers first, then find HCF of that result with the third number
HCF is always less than or equal to the smallest number

Practice these HCF problems to master the concepts!

Gyankatta Math Learning Resource • HCF Practice