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 497, 672, 63 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 497, 672, 63 is 7 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 497, 672, 63 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 497, 672, 63 is 7.
HCF(497, 672, 63) = 7
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 497, 672, 63 is 7.
Step 1: Since 672 > 497, we apply the division lemma to 672 and 497, to get
672 = 497 x 1 + 175
Step 2: Since the reminder 497 ≠ 0, we apply division lemma to 175 and 497, to get
497 = 175 x 2 + 147
Step 3: We consider the new divisor 175 and the new remainder 147, and apply the division lemma to get
175 = 147 x 1 + 28
We consider the new divisor 147 and the new remainder 28,and apply the division lemma to get
147 = 28 x 5 + 7
We consider the new divisor 28 and the new remainder 7,and apply the division lemma to get
28 = 7 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 497 and 672 is 7
Notice that 7 = HCF(28,7) = HCF(147,28) = HCF(175,147) = HCF(497,175) = HCF(672,497) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 63 > 7, we apply the division lemma to 63 and 7, to get
63 = 7 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 7 and 63 is 7
Notice that 7 = HCF(63,7) .
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 497, 672, 63?
Answer: HCF of 497, 672, 63 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 497, 672, 63 using Euclid's Algorithm?
Answer: For arbitrary numbers 497, 672, 63 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.