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 945, 105, 252 i.e. 21 the largest integer that leaves a remainder zero for all numbers.
HCF of 945, 105, 252 is 21 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 945, 105, 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 945, 105, 252 is 21.
HCF(945, 105, 252) = 21
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 945, 105, 252 is 21.
Step 1: Since 945 > 105, we apply the division lemma to 945 and 105, to get
945 = 105 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 105, the HCF of 945 and 105 is 105
Notice that 105 = HCF(945,105) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 252 > 105, we apply the division lemma to 252 and 105, to get
252 = 105 x 2 + 42
Step 2: Since the reminder 105 ≠ 0, we apply division lemma to 42 and 105, to get
105 = 42 x 2 + 21
Step 3: We consider the new divisor 42 and the new remainder 21, and apply the division lemma to get
42 = 21 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 21, the HCF of 105 and 252 is 21
Notice that 21 = HCF(42,21) = HCF(105,42) = HCF(252,105) .
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 945, 105, 252?
Answer: HCF of 945, 105, 252 is 21 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 945, 105, 252 using Euclid's Algorithm?
Answer: For arbitrary numbers 945, 105, 252 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.