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 884, 765, 542 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 884, 765, 542 is 1 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 884, 765, 542 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 884, 765, 542 is 1.
HCF(884, 765, 542) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 884, 765, 542 is 1.
Step 1: Since 884 > 765, we apply the division lemma to 884 and 765, to get
884 = 765 x 1 + 119
Step 2: Since the reminder 765 ≠ 0, we apply division lemma to 119 and 765, to get
765 = 119 x 6 + 51
Step 3: We consider the new divisor 119 and the new remainder 51, and apply the division lemma to get
119 = 51 x 2 + 17
We consider the new divisor 51 and the new remainder 17, and apply the division lemma to get
51 = 17 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 17, the HCF of 884 and 765 is 17
Notice that 17 = HCF(51,17) = HCF(119,51) = HCF(765,119) = HCF(884,765) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 542 > 17, we apply the division lemma to 542 and 17, to get
542 = 17 x 31 + 15
Step 2: Since the reminder 17 ≠ 0, we apply division lemma to 15 and 17, to get
17 = 15 x 1 + 2
Step 3: We consider the new divisor 15 and the new remainder 2, and apply the division lemma to get
15 = 2 x 7 + 1
We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 17 and 542 is 1
Notice that 1 = HCF(2,1) = HCF(15,2) = HCF(17,15) = HCF(542,17) .
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 884, 765, 542?
Answer: HCF of 884, 765, 542 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 884, 765, 542 using Euclid's Algorithm?
Answer: For arbitrary numbers 884, 765, 542 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.