Highest Common Factor of 137, 762, 899, 103 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 137, 762, 899, 103 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 137, 762, 899, 103 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 137, 762, 899, 103 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 137, 762, 899, 103 is 1.
HCF(137, 762, 899, 103) = 1
HCF of 137, 762, 899, 103 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 137, 762, 899, 103 is 1.
Highest Common Factor of 137,762,899,103 is 1
Step 1: Since 762 > 137, we apply the division lemma to 762 and 137, to get
762 = 137 x 5 + 77
Step 2: Since the reminder 137 ≠ 0, we apply division lemma to 77 and 137, to get
137 = 77 x 1 + 60
Step 3: We consider the new divisor 77 and the new remainder 60, and apply the division lemma to get
77 = 60 x 1 + 17
We consider the new divisor 60 and the new remainder 17,and apply the division lemma to get
60 = 17 x 3 + 9
We consider the new divisor 17 and the new remainder 9,and apply the division lemma to get
17 = 9 x 1 + 8
We consider the new divisor 9 and the new remainder 8,and apply the division lemma to get
9 = 8 x 1 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 137 and 762 is 1
Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(17,9) = HCF(60,17) = HCF(77,60) = HCF(137,77) = HCF(762,137) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 899 > 1, we apply the division lemma to 899 and 1, to get
899 = 1 x 899 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 899 is 1
Notice that 1 = HCF(899,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 103 > 1, we apply the division lemma to 103 and 1, to get
103 = 1 x 103 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 103 is 1
Notice that 1 = HCF(103,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 137, 762, 899, 103 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 137, 762, 899, 103?
Answer: HCF of 137, 762, 899, 103 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 137, 762, 899, 103 using Euclid's Algorithm?
Answer: For arbitrary numbers 137, 762, 899, 103 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.