Highest Common Factor of 109, 407, 374 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 109, 407, 374 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 109, 407, 374 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 109, 407, 374 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 109, 407, 374 is 1.
HCF(109, 407, 374) = 1
HCF of 109, 407, 374 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 109, 407, 374 is 1.
Highest Common Factor of 109,407,374 is 1
Step 1: Since 407 > 109, we apply the division lemma to 407 and 109, to get
407 = 109 x 3 + 80
Step 2: Since the reminder 109 ≠ 0, we apply division lemma to 80 and 109, to get
109 = 80 x 1 + 29
Step 3: We consider the new divisor 80 and the new remainder 29, and apply the division lemma to get
80 = 29 x 2 + 22
We consider the new divisor 29 and the new remainder 22,and apply the division lemma to get
29 = 22 x 1 + 7
We consider the new divisor 22 and the new remainder 7,and apply the division lemma to get
22 = 7 x 3 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 109 and 407 is 1
Notice that 1 = HCF(7,1) = HCF(22,7) = HCF(29,22) = HCF(80,29) = HCF(109,80) = HCF(407,109) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 374 > 1, we apply the division lemma to 374 and 1, to get
374 = 1 x 374 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 374 is 1
Notice that 1 = HCF(374,1) .
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Frequently Asked Questions on HCF of 109, 407, 374 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 109, 407, 374?
Answer: HCF of 109, 407, 374 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 109, 407, 374 using Euclid's Algorithm?
Answer: For arbitrary numbers 109, 407, 374 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.