Highest Common Factor of 312, 520, 930, 38 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 312, 520, 930, 38 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 312, 520, 930, 38 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 312, 520, 930, 38 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 312, 520, 930, 38 is 2.
HCF(312, 520, 930, 38) = 2
HCF of 312, 520, 930, 38 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 312, 520, 930, 38 is 2.
Highest Common Factor of 312,520,930,38 is 2
Step 1: Since 520 > 312, we apply the division lemma to 520 and 312, to get
520 = 312 x 1 + 208
Step 2: Since the reminder 312 ≠ 0, we apply division lemma to 208 and 312, to get
312 = 208 x 1 + 104
Step 3: We consider the new divisor 208 and the new remainder 104, and apply the division lemma to get
208 = 104 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 104, the HCF of 312 and 520 is 104
Notice that 104 = HCF(208,104) = HCF(312,208) = HCF(520,312) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 930 > 104, we apply the division lemma to 930 and 104, to get
930 = 104 x 8 + 98
Step 2: Since the reminder 104 ≠ 0, we apply division lemma to 98 and 104, to get
104 = 98 x 1 + 6
Step 3: We consider the new divisor 98 and the new remainder 6, and apply the division lemma to get
98 = 6 x 16 + 2
We consider the new divisor 6 and the new remainder 2, and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 104 and 930 is 2
Notice that 2 = HCF(6,2) = HCF(98,6) = HCF(104,98) = HCF(930,104) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 38 > 2, we apply the division lemma to 38 and 2, to get
38 = 2 x 19 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 38 is 2
Notice that 2 = HCF(38,2) .
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Frequently Asked Questions on HCF of 312, 520, 930, 38 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 312, 520, 930, 38?
Answer: HCF of 312, 520, 930, 38 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 312, 520, 930, 38 using Euclid's Algorithm?
Answer: For arbitrary numbers 312, 520, 930, 38 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.