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 108, 945, 567 i.e. 27 the largest integer that leaves a remainder zero for all numbers.
HCF of 108, 945, 567 is 27 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 108, 945, 567 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 108, 945, 567 is 27.
HCF(108, 945, 567) = 27
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 108, 945, 567 is 27.
Step 1: Since 945 > 108, we apply the division lemma to 945 and 108, to get
945 = 108 x 8 + 81
Step 2: Since the reminder 108 ≠ 0, we apply division lemma to 81 and 108, to get
108 = 81 x 1 + 27
Step 3: We consider the new divisor 81 and the new remainder 27, and apply the division lemma to get
81 = 27 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 27, the HCF of 108 and 945 is 27
Notice that 27 = HCF(81,27) = HCF(108,81) = HCF(945,108) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 567 > 27, we apply the division lemma to 567 and 27, to get
567 = 27 x 21 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 27, the HCF of 27 and 567 is 27
Notice that 27 = HCF(567,27) .
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 108, 945, 567?
Answer: HCF of 108, 945, 567 is 27 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 108, 945, 567 using Euclid's Algorithm?
Answer: For arbitrary numbers 108, 945, 567 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.