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 532, 942, 108 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 532, 942, 108 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 532, 942, 108 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 532, 942, 108 is 2.
HCF(532, 942, 108) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 532, 942, 108 is 2.
Step 1: Since 942 > 532, we apply the division lemma to 942 and 532, to get
942 = 532 x 1 + 410
Step 2: Since the reminder 532 ≠ 0, we apply division lemma to 410 and 532, to get
532 = 410 x 1 + 122
Step 3: We consider the new divisor 410 and the new remainder 122, and apply the division lemma to get
410 = 122 x 3 + 44
We consider the new divisor 122 and the new remainder 44,and apply the division lemma to get
122 = 44 x 2 + 34
We consider the new divisor 44 and the new remainder 34,and apply the division lemma to get
44 = 34 x 1 + 10
We consider the new divisor 34 and the new remainder 10,and apply the division lemma to get
34 = 10 x 3 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 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 532 and 942 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(34,10) = HCF(44,34) = HCF(122,44) = HCF(410,122) = HCF(532,410) = HCF(942,532) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 108 > 2, we apply the division lemma to 108 and 2, to get
108 = 2 x 54 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 108 is 2
Notice that 2 = HCF(108,2) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 532, 942, 108?
Answer: HCF of 532, 942, 108 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 532, 942, 108 using Euclid's Algorithm?
Answer: For arbitrary numbers 532, 942, 108 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.