Highest Common Factor of 920, 840, 112, 346 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 920, 840, 112, 346 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 920, 840, 112, 346 is 2 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 920, 840, 112, 346 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 920, 840, 112, 346 is 2.
HCF(920, 840, 112, 346) = 2
HCF of 920, 840, 112, 346 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 920, 840, 112, 346 is 2.
Highest Common Factor of 920,840,112,346 is 2
Step 1: Since 920 > 840, we apply the division lemma to 920 and 840, to get
920 = 840 x 1 + 80
Step 2: Since the reminder 840 ≠ 0, we apply division lemma to 80 and 840, to get
840 = 80 x 10 + 40
Step 3: We consider the new divisor 80 and the new remainder 40, and apply the division lemma to get
80 = 40 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 40, the HCF of 920 and 840 is 40
Notice that 40 = HCF(80,40) = HCF(840,80) = HCF(920,840) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 112 > 40, we apply the division lemma to 112 and 40, to get
112 = 40 x 2 + 32
Step 2: Since the reminder 40 ≠ 0, we apply division lemma to 32 and 40, to get
40 = 32 x 1 + 8
Step 3: We consider the new divisor 32 and the new remainder 8, and apply the division lemma to get
32 = 8 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 40 and 112 is 8
Notice that 8 = HCF(32,8) = HCF(40,32) = HCF(112,40) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 346 > 8, we apply the division lemma to 346 and 8, to get
346 = 8 x 43 + 2
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 2 and 8, to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8 and 346 is 2
Notice that 2 = HCF(8,2) = HCF(346,8) .
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Frequently Asked Questions on HCF of 920, 840, 112, 346 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 920, 840, 112, 346?
Answer: HCF of 920, 840, 112, 346 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 920, 840, 112, 346 using Euclid's Algorithm?
Answer: For arbitrary numbers 920, 840, 112, 346 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.