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 428, 308, 994 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 428, 308, 994 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 428, 308, 994 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 428, 308, 994 is 2.
HCF(428, 308, 994) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 428, 308, 994 is 2.
Step 1: Since 428 > 308, we apply the division lemma to 428 and 308, to get
428 = 308 x 1 + 120
Step 2: Since the reminder 308 ≠ 0, we apply division lemma to 120 and 308, to get
308 = 120 x 2 + 68
Step 3: We consider the new divisor 120 and the new remainder 68, and apply the division lemma to get
120 = 68 x 1 + 52
We consider the new divisor 68 and the new remainder 52,and apply the division lemma to get
68 = 52 x 1 + 16
We consider the new divisor 52 and the new remainder 16,and apply the division lemma to get
52 = 16 x 3 + 4
We consider the new divisor 16 and the new remainder 4,and apply the division lemma to get
16 = 4 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 428 and 308 is 4
Notice that 4 = HCF(16,4) = HCF(52,16) = HCF(68,52) = HCF(120,68) = HCF(308,120) = HCF(428,308) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 994 > 4, we apply the division lemma to 994 and 4, to get
994 = 4 x 248 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4 and 994 is 2
Notice that 2 = HCF(4,2) = HCF(994,4) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 428, 308, 994?
Answer: HCF of 428, 308, 994 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 428, 308, 994 using Euclid's Algorithm?
Answer: For arbitrary numbers 428, 308, 994 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.