Highest Common Factor of 374, 991, 623, 820 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 374, 991, 623, 820 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 374, 991, 623, 820 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 374, 991, 623, 820 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 374, 991, 623, 820 is 1.
HCF(374, 991, 623, 820) = 1
HCF of 374, 991, 623, 820 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 374, 991, 623, 820 is 1.
Highest Common Factor of 374,991,623,820 is 1
Step 1: Since 991 > 374, we apply the division lemma to 991 and 374, to get
991 = 374 x 2 + 243
Step 2: Since the reminder 374 ≠ 0, we apply division lemma to 243 and 374, to get
374 = 243 x 1 + 131
Step 3: We consider the new divisor 243 and the new remainder 131, and apply the division lemma to get
243 = 131 x 1 + 112
We consider the new divisor 131 and the new remainder 112,and apply the division lemma to get
131 = 112 x 1 + 19
We consider the new divisor 112 and the new remainder 19,and apply the division lemma to get
112 = 19 x 5 + 17
We consider the new divisor 19 and the new remainder 17,and apply the division lemma to get
19 = 17 x 1 + 2
We consider the new divisor 17 and the new remainder 2,and apply the division lemma to get
17 = 2 x 8 + 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 374 and 991 is 1
Notice that 1 = HCF(2,1) = HCF(17,2) = HCF(19,17) = HCF(112,19) = HCF(131,112) = HCF(243,131) = HCF(374,243) = HCF(991,374) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 623 > 1, we apply the division lemma to 623 and 1, to get
623 = 1 x 623 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 623 is 1
Notice that 1 = HCF(623,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 820 > 1, we apply the division lemma to 820 and 1, to get
820 = 1 x 820 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 820 is 1
Notice that 1 = HCF(820,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 374, 991, 623, 820 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 374, 991, 623, 820?
Answer: HCF of 374, 991, 623, 820 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 374, 991, 623, 820 using Euclid's Algorithm?
Answer: For arbitrary numbers 374, 991, 623, 820 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.