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 378, 644, 994 i.e. 14 the largest integer that leaves a remainder zero for all numbers.
HCF of 378, 644, 994 is 14 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 378, 644, 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 378, 644, 994 is 14.
HCF(378, 644, 994) = 14
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 378, 644, 994 is 14.
Step 1: Since 644 > 378, we apply the division lemma to 644 and 378, to get
644 = 378 x 1 + 266
Step 2: Since the reminder 378 ≠ 0, we apply division lemma to 266 and 378, to get
378 = 266 x 1 + 112
Step 3: We consider the new divisor 266 and the new remainder 112, and apply the division lemma to get
266 = 112 x 2 + 42
We consider the new divisor 112 and the new remainder 42,and apply the division lemma to get
112 = 42 x 2 + 28
We consider the new divisor 42 and the new remainder 28,and apply the division lemma to get
42 = 28 x 1 + 14
We consider the new divisor 28 and the new remainder 14,and apply the division lemma to get
28 = 14 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 378 and 644 is 14
Notice that 14 = HCF(28,14) = HCF(42,28) = HCF(112,42) = HCF(266,112) = HCF(378,266) = HCF(644,378) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 994 > 14, we apply the division lemma to 994 and 14, to get
994 = 14 x 71 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 14 and 994 is 14
Notice that 14 = HCF(994,14) .
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 378, 644, 994?
Answer: HCF of 378, 644, 994 is 14 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 378, 644, 994 using Euclid's Algorithm?
Answer: For arbitrary numbers 378, 644, 994 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.