Highest Common Factor of 324, 972, 930, 924 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 324, 972, 930, 924 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 324, 972, 930, 924 is 6 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 324, 972, 930, 924 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 324, 972, 930, 924 is 6.
HCF(324, 972, 930, 924) = 6
HCF of 324, 972, 930, 924 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 324, 972, 930, 924 is 6.
Highest Common Factor of 324,972,930,924 is 6
Step 1: Since 972 > 324, we apply the division lemma to 972 and 324, to get
972 = 324 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 324, the HCF of 324 and 972 is 324
Notice that 324 = HCF(972,324) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 930 > 324, we apply the division lemma to 930 and 324, to get
930 = 324 x 2 + 282
Step 2: Since the reminder 324 ≠ 0, we apply division lemma to 282 and 324, to get
324 = 282 x 1 + 42
Step 3: We consider the new divisor 282 and the new remainder 42, and apply the division lemma to get
282 = 42 x 6 + 30
We consider the new divisor 42 and the new remainder 30,and apply the division lemma to get
42 = 30 x 1 + 12
We consider the new divisor 30 and the new remainder 12,and apply the division lemma to get
30 = 12 x 2 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 324 and 930 is 6
Notice that 6 = HCF(12,6) = HCF(30,12) = HCF(42,30) = HCF(282,42) = HCF(324,282) = HCF(930,324) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 924 > 6, we apply the division lemma to 924 and 6, to get
924 = 6 x 154 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 6 and 924 is 6
Notice that 6 = HCF(924,6) .
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Frequently Asked Questions on HCF of 324, 972, 930, 924 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 324, 972, 930, 924?
Answer: HCF of 324, 972, 930, 924 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 324, 972, 930, 924 using Euclid's Algorithm?
Answer: For arbitrary numbers 324, 972, 930, 924 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.