Highest Common Factor of 310, 222, 640 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 310, 222, 640 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 310, 222, 640 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 310, 222, 640 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 310, 222, 640 is 2.
HCF(310, 222, 640) = 2
HCF of 310, 222, 640 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 310, 222, 640 is 2.
Highest Common Factor of 310,222,640 is 2
Step 1: Since 310 > 222, we apply the division lemma to 310 and 222, to get
310 = 222 x 1 + 88
Step 2: Since the reminder 222 ≠ 0, we apply division lemma to 88 and 222, to get
222 = 88 x 2 + 46
Step 3: We consider the new divisor 88 and the new remainder 46, and apply the division lemma to get
88 = 46 x 1 + 42
We consider the new divisor 46 and the new remainder 42,and apply the division lemma to get
46 = 42 x 1 + 4
We consider the new divisor 42 and the new remainder 4,and apply the division lemma to get
42 = 4 x 10 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 310 and 222 is 2
Notice that 2 = HCF(4,2) = HCF(42,4) = HCF(46,42) = HCF(88,46) = HCF(222,88) = HCF(310,222) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 640 > 2, we apply the division lemma to 640 and 2, to get
640 = 2 x 320 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 640 is 2
Notice that 2 = HCF(640,2) .
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Frequently Asked Questions on HCF of 310, 222, 640 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 310, 222, 640?
Answer: HCF of 310, 222, 640 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 310, 222, 640 using Euclid's Algorithm?
Answer: For arbitrary numbers 310, 222, 640 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
