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 377, 993, 715 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 377, 993, 715 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 377, 993, 715 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 377, 993, 715 is 1.
HCF(377, 993, 715) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 377, 993, 715 is 1.
Step 1: Since 993 > 377, we apply the division lemma to 993 and 377, to get
993 = 377 x 2 + 239
Step 2: Since the reminder 377 ≠ 0, we apply division lemma to 239 and 377, to get
377 = 239 x 1 + 138
Step 3: We consider the new divisor 239 and the new remainder 138, and apply the division lemma to get
239 = 138 x 1 + 101
We consider the new divisor 138 and the new remainder 101,and apply the division lemma to get
138 = 101 x 1 + 37
We consider the new divisor 101 and the new remainder 37,and apply the division lemma to get
101 = 37 x 2 + 27
We consider the new divisor 37 and the new remainder 27,and apply the division lemma to get
37 = 27 x 1 + 10
We consider the new divisor 27 and the new remainder 10,and apply the division lemma to get
27 = 10 x 2 + 7
We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get
10 = 7 x 1 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 377 and 993 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(27,10) = HCF(37,27) = HCF(101,37) = HCF(138,101) = HCF(239,138) = HCF(377,239) = HCF(993,377) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 715 > 1, we apply the division lemma to 715 and 1, to get
715 = 1 x 715 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 715 is 1
Notice that 1 = HCF(715,1) .
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 377, 993, 715?
Answer: HCF of 377, 993, 715 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 377, 993, 715 using Euclid's Algorithm?
Answer: For arbitrary numbers 377, 993, 715 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.