Highest Common Factor of 346, 972, 331, 656 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 346, 972, 331, 656 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 346, 972, 331, 656 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 346, 972, 331, 656 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 346, 972, 331, 656 is 1.
HCF(346, 972, 331, 656) = 1
HCF of 346, 972, 331, 656 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 346, 972, 331, 656 is 1.
Highest Common Factor of 346,972,331,656 is 1
Step 1: Since 972 > 346, we apply the division lemma to 972 and 346, to get
972 = 346 x 2 + 280
Step 2: Since the reminder 346 ≠ 0, we apply division lemma to 280 and 346, to get
346 = 280 x 1 + 66
Step 3: We consider the new divisor 280 and the new remainder 66, and apply the division lemma to get
280 = 66 x 4 + 16
We consider the new divisor 66 and the new remainder 16,and apply the division lemma to get
66 = 16 x 4 + 2
We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 346 and 972 is 2
Notice that 2 = HCF(16,2) = HCF(66,16) = HCF(280,66) = HCF(346,280) = HCF(972,346) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 331 > 2, we apply the division lemma to 331 and 2, to get
331 = 2 x 165 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 331 is 1
Notice that 1 = HCF(2,1) = HCF(331,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 656 > 1, we apply the division lemma to 656 and 1, to get
656 = 1 x 656 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 656 is 1
Notice that 1 = HCF(656,1) .
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Frequently Asked Questions on HCF of 346, 972, 331, 656 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 346, 972, 331, 656?
Answer: HCF of 346, 972, 331, 656 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 346, 972, 331, 656 using Euclid's Algorithm?
Answer: For arbitrary numbers 346, 972, 331, 656 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.