Highest Common Factor of 39, 108, 840, 252 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 39, 108, 840, 252 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 39, 108, 840, 252 is 3 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 39, 108, 840, 252 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 39, 108, 840, 252 is 3.
HCF(39, 108, 840, 252) = 3
HCF of 39, 108, 840, 252 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 39, 108, 840, 252 is 3.
Highest Common Factor of 39,108,840,252 is 3
Step 1: Since 108 > 39, we apply the division lemma to 108 and 39, to get
108 = 39 x 2 + 30
Step 2: Since the reminder 39 ≠ 0, we apply division lemma to 30 and 39, to get
39 = 30 x 1 + 9
Step 3: We consider the new divisor 30 and the new remainder 9, and apply the division lemma to get
30 = 9 x 3 + 3
We consider the new divisor 9 and the new remainder 3, and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 39 and 108 is 3
Notice that 3 = HCF(9,3) = HCF(30,9) = HCF(39,30) = HCF(108,39) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 840 > 3, we apply the division lemma to 840 and 3, to get
840 = 3 x 280 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 840 is 3
Notice that 3 = HCF(840,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 252 > 3, we apply the division lemma to 252 and 3, to get
252 = 3 x 84 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 252 is 3
Notice that 3 = HCF(252,3) .
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Frequently Asked Questions on HCF of 39, 108, 840, 252 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 39, 108, 840, 252?
Answer: HCF of 39, 108, 840, 252 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 39, 108, 840, 252 using Euclid's Algorithm?
Answer: For arbitrary numbers 39, 108, 840, 252 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.