Highest Common Factor of 120, 998, 40 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 120, 998, 40 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 120, 998, 40 is 2 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 120, 998, 40 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 120, 998, 40 is 2.
HCF(120, 998, 40) = 2
HCF of 120, 998, 40 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 120, 998, 40 is 2.
Highest Common Factor of 120,998,40 is 2
Step 1: Since 998 > 120, we apply the division lemma to 998 and 120, to get
998 = 120 x 8 + 38
Step 2: Since the reminder 120 ≠ 0, we apply division lemma to 38 and 120, to get
120 = 38 x 3 + 6
Step 3: We consider the new divisor 38 and the new remainder 6, and apply the division lemma to get
38 = 6 x 6 + 2
We consider the new divisor 6 and the new remainder 2, and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 120 and 998 is 2
Notice that 2 = HCF(6,2) = HCF(38,6) = HCF(120,38) = HCF(998,120) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 40 > 2, we apply the division lemma to 40 and 2, to get
40 = 2 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 40 is 2
Notice that 2 = HCF(40,2) .
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Frequently Asked Questions on HCF of 120, 998, 40 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 120, 998, 40?
Answer: HCF of 120, 998, 40 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 120, 998, 40 using Euclid's Algorithm?
Answer: For arbitrary numbers 120, 998, 40 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.