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 634, 751, 996 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 634, 751, 996 is 1 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 634, 751, 996 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 634, 751, 996 is 1.
HCF(634, 751, 996) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 634, 751, 996 is 1.
Step 1: Since 751 > 634, we apply the division lemma to 751 and 634, to get
751 = 634 x 1 + 117
Step 2: Since the reminder 634 ≠ 0, we apply division lemma to 117 and 634, to get
634 = 117 x 5 + 49
Step 3: We consider the new divisor 117 and the new remainder 49, and apply the division lemma to get
117 = 49 x 2 + 19
We consider the new divisor 49 and the new remainder 19,and apply the division lemma to get
49 = 19 x 2 + 11
We consider the new divisor 19 and the new remainder 11,and apply the division lemma to get
19 = 11 x 1 + 8
We consider the new divisor 11 and the new remainder 8,and apply the division lemma to get
11 = 8 x 1 + 3
We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get
8 = 3 x 2 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 634 and 751 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(11,8) = HCF(19,11) = HCF(49,19) = HCF(117,49) = HCF(634,117) = HCF(751,634) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 996 > 1, we apply the division lemma to 996 and 1, to get
996 = 1 x 996 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 996 is 1
Notice that 1 = HCF(996,1) .
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 634, 751, 996?
Answer: HCF of 634, 751, 996 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 634, 751, 996 using Euclid's Algorithm?
Answer: For arbitrary numbers 634, 751, 996 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.